Efficient multicast delivery for data redundancy minimization over wireless data centers

IEEE TRANSACTIONS ON
EMERGING TOPICS
IN COMPUTING
Received 1 December 2014; revised 13 February 2015; accepted 5 May 2015.
Date of Publication 14 May 2015; date of current version 8 June 2016.
Digital Object Identifier 10.1109/TETC.2015.2433936
Efficient Multicast Delivery for Data
Redundancy Minimization Over
Wireless Data Centers
CHING-CHIH CHUANG1, (Student Member, IEEE), YA-JU YU2,
AI-CHUN PANG1,3,4, (Senior Member, IEEE), HSUEH-WEN TSENG5, (Member, IEEE),
and HSIN-PENG LIN1,6
1Department of Computer Science and Information Engineering, National Taiwan University, Taipei 10617, Taiwan
2Smart Network System Institute, Institute for Information Industry, Taipei 106, Taiwan
3Research Center for Information Technology Innovation, Academia Sinica, Taipei 115, Taiwan
4Graduate Institute of Networking and Multimedia, National Taiwan University, Taipei 10617, Taiwan
5Department of Computer Science and Engineering, National Chung Hsing University, Taichung 402, Taiwan
6Telecommunication Laboratories, Chunghwa Telecom Company, Ltd., Taipei 235, Taiwan
CORRESPONDING AUTHOR: A.-C. PANG (acpang@csie.ntu.edu.tw)
This work was supported in part by the Excellent Research Projects of National Taiwan University under Grant 104R890822,
in part by the Ministry of Science and Technology under Grant 102-2221-E-002-075-MY2, Grant 103-2221-E-002-142-MY3,
and Grant 102-2221-E-005-037-MY2, in part by the Information and Communications Research Laboratories,
in part by the Industrial Technology Research Institute, in part by the Institute for Information Industry, and
in part by the Research Center for Information Technology Innovation, Academia Sinica.
ABSTRACT With the explosive growth of cloud-based services, large-scale data centers are widely
built for housing critical computing resources to gain significant economic benefits. In data centers, the
cloud services are generally accomplished by multicast-based group communications. Recently, many
well-known industries, such as Microsoft, Google, and IBM, adopt high-speed wireless technologies to
augment network capacity in data centers. However, those well-known multicast delivery schemes for
traditional wired data centers do not consider the unique characteristics of wireless communications, which
may result in unnecessary data transmissions and network congestions. Under the coexisting scenario of wired
and wireless links, this paper studies multicast tree construction and maintenance problems. The objective is
to minimize the total multicast traffic. We prove the problems are NP-hard and propose efficient heuristic
algorithms for the two problems. Based on real traces and practical settings obtained from commercial data
centers, a series of experiments are conducted, and the experimental results show that our proposed algorithms
are effective for reducing multicast data traffic. The results also provide useful insights into the design of
multicast tree construction and maintenance for wireless data center networks.
INDEX TERMS Data redundancy, multicast, wireless data centers.
I. INTRODUCTION
With the explosive growth of cloud-based services,
large-scale data centers are widely built for housing critical
computing resources to gain significant economic benefits.
In data center networks, the cloud-based services are mostly
accomplished by group communications with multicast
traffic. For instance, a web server redirects queries to a
set of indexing servers. Distributed file systems replicate
file chunks to a set of storage nodes [1]. For distributed
execution engines such as MapReduce [2], the master node
assigns tasks to a group of servers for cooperative compu-
tations. In social networks (e.g., Facebook, Twitter, etc) [3],
users frequently share their messages, photos and videos with
their friends, and group communications are also needed.
In group communications, a source node has to transmit one
copy of the data to multiple destination nodes. If the same
data is dispersedly transmitted by different links to different
destinations, the multicast traffic will occupy a large portion
of network resources, which results in network congestions.
According to the measurements reported by Microsoft, the
number of multicast groups in a data center is large and each
group generally comprises numerous multicast members [4];
the data traffic in top-of-rack switches is heavy and may cause
serious degradation in network performance [5].
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IN COMPUTING Chuang et al.: Efficient Multicast Delivery for Data Redundancy Minimization
To effectively accommodate the huge amount of data
traffic in data center networks, high-speed wireless
technologies (e.g., 802.11ad 60GHz wireless transmissions)
are considered, in existing wired data centers such as
Microsoft [6], Google [7], and IBM [8], to be used on top-of-
rack switches to augment network capacity and provide fast
connectivity. Specifically, in [9], a comprehensive analysis
demonstrates that the hybrid structure, where wireless access
points and wired switches coexist, is a feasible solution
for data centers. In such the wireless data center, multicast
data can be transmitted by either wireless access points or
wired switches. Although wireless medium is broadcast in
nature and might be more suitable for multicast, how to
build multicast trees in wireless data centers is complicated
and faces many challenges. The challenges mainly come
from the following factors. 1) Since wireless access points
are densely deployed in data centers, the interference issue
among wireless access points should be carefully considered.
2) Unlike a wired switch, a wireless access point can transmit
data to more than one access point in its communication range
and has more selections for transmission paths, especially
when a directional antenna is adopted [5]. 3) The coexistence
of wired and wireless links lead to the interesting issue that
how to avoid wireless interference by adopting wired links
in wireless data centers such that more wireless access points
can be transmitted simultaneously.
In addition to the above challenges, the cloud services such
as social networks and VM migration have some receivers
dynamically joining and leaving their multicast groups so
their multicast trees have to be reconstructed when the events
occur. The tree reconstruction in this case will cause a
‘‘chain reaction’’. That is, the changes will be made not
only for the groups (abbreviated as ‘‘involved groups’’) with
member joining and leaving, but also for the groups
(abbreviated as ‘‘victim groups’’) which are affected by
‘‘involved groups’’ due to wireless interference. A trivial way
to avoid wireless interference is to switch the affected trans-
missions from wireless to wired links, which will definitely
generate a large amount of redundant multicast data traffic.
Alternatively, an exhausting computation and excessive
signaling exchanges for overall tree reconstruction need to
be done to minimize the redundancy. Thus how to efficiently
transmit multicast data while maintaining low computation
without involving too many multicast trees should be
carefully studied. We will give two simple examples
in Section III to respectively describe the above mentioned
challenging issues for wireless data center networks in more
details.
In this paper, we address the group communication issues,
multicast tree building and maintenance, raised in wireless
data center networks comprised of wired and wireless links.
The objective is to minimize the total multicast data traffic.
The contributions of this paper are as follows. Firstly,
we formulate the multicast tree building and maintenance
problems with the consideration of coexisting wired and
wireless links in wireless data center networks. We prove
that the target problems are NP-hard. For the tree building
problem, we propose a heuristic algorithm to efficiently
use wireless transmission links. For the tree maintenance
problem, a low-complexity solution is presented to
reconstruct the multicast trees when receivers join or leave.
Finally, we conduct a series of simulations based on prac-
tical parameter settings to evaluate the performance of our
proposed algorithms. We collect real traces of MapReduce
from the largest telecom operator in Taiwan and refer to
their data center topology for our simulation setup. The
simulation results demonstrate that our proposed algorithms
are very effective in reducing the total data redundancy of
the multicast traffic. The results also provide useful insights
into the design of multicast tree building and maintenance for
wireless data center networks.
The rest of the paper is organized as follows. In Section II,
we review some related works on multicast tree construction
and maintenance. Section III describes our system model
and formulates the problems. In Section IV and V, we prove
that our target problems are NP-hard and propose effi-
cient heuristic solutions. Simulation results are presented in
Section VI. Section VII concludes the paper.
II. RELATED WORKS
To achieve group communications, multicast is used to
transmit data to a group of destinations. The first standard of
IP (Internet Protocol) multicast is specified in RFC 1112 [10].
Then the Internet Group Management Protocol (IGMP) is
defined to allow a host to join and leave a group, and to
report its IP multicast group membership to neighboring
multicast routers [11]. The tree structure is commonly
adopted for multicast to reduce redundant data transmissions
and avoid unnecessary network resource usage. The
multicast tree can be built by the two methods, source-based
and share-based [12]. The source-based tree is established
by the shortest-path algorithm, and each sender requires an
individual tree to transmit its multicast data. This implies
that the source-based multicast tree is more suitable for the
applications with few senders in a multicast group. In con-
trast, only one shared-based tree is needed for a multicast
group. Multiple senders in a common multicast group can
share the tree. However, for both source-based and shared-
based multicast trees, the tree establishment and maintenance
procedures generally follow the receiver-driven manner,
which would result in redundant transmission links especially
when there are multiple disjoint equal-cost paths between a
pair of servers in wired data center networks [13].
For wireless ad-hoc networks, multicast routing has been
widely studied [14], and can be roughly classified into
tree-based, mesh-based, and hybrid-based approaches. The
tree-based approach establishes a single path between any
two nodes in a multicast group [15]. Since ad-hoc nodes can
move freely, the tree needs to be frequently re-established due
to link failure such that packet delivery ratio is decreased.
Thus, some studies, see [16], proposed the meshed-based
approach to provide multiple paths for robust connectivity for
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Chuang et al.: Efficient Multicast Delivery for Data Redundancy Minimization
EMERGING TOPICS
IN COMPUTING
group communications. However, massive control messages
used to update topology information and redundant paths
consume a large portion of network resources. Consequently,
hybrid-based multicast routing protocols, see [17], were
proposed. The above wireless multicast routing approaches
cannot be applied to wireless data center networks, since they
do not consider how to build and maintain multicast trees
when wired and wireless links co-exist.
Recently, some researches have paid attention to multicast
issues in traditional wired data centers. In [18], considering
the hardware constraint in supporting multicast operations in
switches, Vigfusson et al. developed a mechanism to select
parts of group communication requests to adopt multicast
delivery while the remaining requests are accomplished by
unicast transmissions. Then, Li et al. [13], [19] observed that
the receiver-driven multicast routing protocols designed for
the Internet do not perform well in terms of the number
of transmission links in densely connected data center
networks with multiple disjoint equal-cost paths. Thus, to
reduce data transmission redundancy for wired data center
networks, an efficient multicast tree establishment and
maintenance approaches were presented for the case that
receivers can dynamically join or leave a multicast group.
However, the approaches do not take wireless links into
account, and only reduce the total number of used wired links,
as their major performance metric, without considering dif-
ferent data rates requested by heterogeneous cloud services.
III. SYSTEM MODEL AND PROBLEM FORMULATION
A. SYSTEM MODEL
In a data center, several servers are grouped in a rack and
each rack is equipped with a switch. The switch is named
as the top-of-rack switch which connects to all the servers
in the rack. Top-of-rack switches are generally connected
by aggregation switches and/or core switches, depending on
their network topology. The types of data center network
topology include hierarchical topology, Fat-tree [20] and
BCube [21]. Considering the deployment cost and complex-
ity of wired links, hierarchical topology is commonly used.
Moreover, many industries [5], [7], [8] are trying to deploy
access points with 60GHz wireless access technologies on
top-of-rack switches to augment network capacity and pro-
vide fast connectivity. The 60GHz access points can support
high data rate with the transmission range of 10 meters.
Since the density of access points is extremely high in data
centers, the access points are generally equipped with the
directional narrow-beam antenna array to mitigate interfer-
ence [6]. Under a managed environment, we assume that
a data center will have a central controller to manage the
forwarding table of switches. The illustration of a simple
wireless data center architecture is shown in Fig. 1, where
there are twelve racks, and each rack has one top-of-rack
switch and one wireless access point. Each top-of-rack switch
connects to an aggregation/core switch by the wired link,
while each top-of-rack access point can transmit data to any
access point within its transmission range.
FIGURE 1. A simple wireless data center architecture.
In wireless data centers, multicast data traffic is delivered
frequently, and tree-based transmission is an effective way to
accomplish the multicast delivery. However, how to build and
maintain multicast trees under the co-existence of wired and
wireless links to minimize redundant multicast traffic in wire-
less data centers is still open and challenging. When multicast
groups are created, we have to construct the corresponding
multicast trees for the groups, referred to as multicast tree
construction problem. On the other hand, when receivers join
or leave a multicast group which has already existed, we
have to reconstruct/maintain the multicast tree, referred to
as multicast tree maintenance problem. The approaches for
constructing and maintaining multicast trees can be classified
into two types [12], source-based and share-based. Since most
of the group communications in data centers have only one
multicast sender, without loss of generality, this paper adopts
the source-based approach.
B. PROBLEM FORMULATION
In this paper, we are interested in the source-based multicast
tree construction and maintenance, comprised of wired and
wireless links in data center networks. The objective is to
minimize the total multicast data traffic (i.e., the transmission
redundancy). The problem formulation is described as
follows. For the sake of brevity, we omit ‘‘∀’’ when the
meaning is clear from the context.
1) THE MULTICAST TREE CONSTRUCTION PROBLEM
A wireless data center is modeled as a directed graph
G = (V, E). The V = (VF , VW ) is a set of racks. Each
rack v ∈ V includes one top-of-rack switch sv ∈ VF and
one wireless access point av ∈ VW. The VF is a set of
top-of-rack switches and VW is a set of top-of-rack access
points. The link set E = (EF , EW ) includes a set of
wired (fixed) links EF and a set of wireless links EW .
Wired link eF
sisj
∈ EF with capacity CF
sisj
(bps) represents
that top-of-rack switch si can transmit data to top-of-rack
switch sj by the wired link. On the other hand, wireless link
eW
axay
∈ EW with capacity CW
axay
(bps) indicates that access
point ax can transmit data to access point ay by the wireless
link.
VOLUME 4, NO. 2, JUNE 2016 227

EMERGING TOPICS
We consider a set of N multicast groups R=(r1, r2, . . . , rN ),
where rk = (νk, Dk, Tk) means that rack νk is the sender of
multicast group k and has to transmit the multicast traffic
with data rate Tk (bps) to a set of destinations (racks)
Dk ⊆ V. Then, we define lF (k, eF
sisj
) ∈ {0, 1} as an indicator
function, which registers 1 if the traffic of multicast group k
passes through wired link eF
sisj
. If wired link eF
sisj
is used
and lF (k, eF
sisj
) is set at 1, top-of-rack switch sj of rack
j ∈ V can receive the multicast data of group k. We also
define lW (k, eW
axay
) ∈ {0, 1} to indicate whether the traffic of
multicast group k uses wireless link eW
axay
or not. If wireless
link eW
axay
is selected and lW (k, eW
axay
) is set at 1, the set of
access points of racks Saxay ⊂ V within the coverage area
of the transmission can overhear and receive the data. Our
purpose is to build a multicast tree, comprised of wired and
wireless links, for each multicast group.
2) THE MULTICAST TREE MAINTENANCE PROBLEM
After the multicast trees are constructed, the problem is to
adjust the tree structure when there are receivers requesting to
join or leave their multicast groups. In addition to the inputs of
the tree construction problem, the tree maintenance problem
are further described as follows. A set of racks Jk and Lk
respectively has nodes requesting to join and leave multicast
group k. Thus, the set of destinations Dk of multicast group k
is changed to (Dk ∪ Jk) Lk. Given the wired and wireless
link indicator functions lF (k, eF
sisj
) and lW (k, eW
axay
) deter-
mined in the multicast tree construction problem, we have to
maintain the multicast tree with wired ˆlF (k, eF
sisj
) and wire-
less link indicator function ˆlW (k, eW
axay
) for each new set of
destinations Dk.
The solutions for the above multicast tree construction and
maintenance are feasible if the following constraints are met.
Note that lF (k, eF
sisj
) and lW (k, eW
axay
) in Equations (1)-(3) is
respectively replaced by ˆlF (k, eF
sisj
) and ˆlW (k, eW
axay
) when the
tree maintenance problem is considered.
a: WIRED LINK CAPACITY CONSTRAINT
In order to avoid over-utilization of top-of-rack switches,
Equation (1) ensures that the data rate of multicast group
through each wired link cannot exceed the available capacity
of each wired link.
N
k=1
Tk · lF
(k, eF
sisj
) + lF
(k, eF
sjsi
) ≤ CF
sisj
, ∀eF
sisj
∈ EF
. (1)
b: ACCESS POINT CAPABILITY CONSTRAINT
Since wireless access points incurs interference from
their neighboring access points, Equation (2) states that
each access point cannot exceed its capability including
interference/data reception (first term) and transmission
(second term). I(ay, eW
axaz
) is used to indicate whether access
point ay is interfered by access point ax, and defined based on
a geometric-based protocol interference model [22]. Based on
the protocol interference model, I(ay, eW
axaz
) = 1 when access
point ay is located in the transmission range of access point ax
for delivering data to access point az.
N
k=1 ax∈VW az∈VW
(
I(ay, eW
axaz
)lW (k, eW
axaz
)Tk
CW
axaz
+
lW (k, eW
ayax
)Tk
CW
ayax
) ≤ 1, ∀ay ∈ VW
, ax = az (2)
where
I(ay, eW
axaz
) =
1, if y ∈ Saxaz
0, otherwise.
c: DELIVERY CONSTRAINT
The destinations of each multicast group must receive their
multicast data.



lW (k,eW
axay )=1
Saxay






lF (k,eF
sisj
)=1
j


 ⊇ Dk, ∀rk ∈ R
(3)
We now define the target problem formally as follows.
3) THE EFFICIENT MULTICAST TREE CONSTRUCTION
PROBLEM
Input instance: Consider a directed graph G = (V, E).
Each wired and wireless link has its capacity CF
sisj
and CW
axay
.
There is a set of N multicast groups R.
Objective: Our objective of this problem is to build a
multicast tree, comprised of wired lF (k, eF
sisj
) and wireless
links lW (k, eW
axay
), for each multicast group such that the mul-
ticast data traffic (data redundancy) of all multicast groups is
minimized. The objective function is expressed as follows.
Min
N
k=1 eF
sisj
∈EF eW
axay ∈EW
Tk × lF
(k, eF
sisj
) + lW
(k, eW
axay
) ,
subject to constraints (1)-(3).
4) THE EFFICIENT MULTICAST TREE MAINTENANCE
PROBLEM
Input instance: Consider a directed graph G = (V, E).
Each wired and wireless link has its capacity CF
sisj
and CW
axay
.
There is a set of N multicast groups R. Given the tree structure
of each multicast group (i.e., wired lF (k, eF
sisj
) and wireless
links lW (k, eW
axay
) ), each multicast group k has a set of nodes
Jk and Lk requesting to join and leave.
Objective: Our objective of this problem is to maintain
each multicast tree, comprised of wired ˆlF (k, eF
sisj
) and wire-
less links ˆlW (k, eW
axay
), for the set of joining and leaving nodes
such that the increased multicast data traffic of all multicast
groups is minimized. The objective function is expressed

EMERGING TOPICS
IN COMPUTING
as follows.
Min
N
k=1 eF
sisj
∈EF eW
axay ∈EW
Tk × ˆlF
(k, eF
sisj
) + ˆlW
(k, eW
axay
)
−
N
k=1 eF
sisj
∈EF eW
axay ∈EW
Tk × lF
(k, eF
sisj
) + lW
(k, eW
axay
) ,
subject to constraints (1)-(3). Table 1 summarizes the
notations used in the problem formulation.
TABLE 1. Summary of notations.
C. AN ILLUSTRATIVE EXAMPLE
1) MULTICAST TREE CONSTRUCTION
We use a simple example, as shown in Fig. 2, to describe the
multicast tree construction problem in wireless data centers.
Consider the wireless data center G shown in Fig. 1. On each
rack, there is a pair of top-of-rack switch and access point.
The data sent from one top-of-rack switch to another should
go through two wired links, while a top-of-rack access
point can directly transmit data to another wireless access
point. Moreover, since the directional antenna is adopted, the
interference range of each access point is limited by its
transmission direction [5]. The capacity of each link is set
as 1Gbps (i.e., CF
sisj
= CW
axay
= 1G, ∀eF
sisj
∈ EF ,
eW axay ∈ EW ). We consider two multicast groups in this
example. For the first multicast group, the sender is placed in
rack 1; the set of destinations includes racks 9, 10, 11, and 12;
and the data rate of the multicast group is set as 1Gbps. For
the second multicast group, the sender is set as rack 4; the
set of destinations includes rack 5, 6, 7, and 8; and the data
rate of the multicast group is 1Gbps. Now, we have to build
a multicast tree, comprised of wired and wireless links, for
each multicast group.
As shown in Fig. 2(a), we only adopt wired links to build
multicast trees as it is for traditional data centers. In this case,
the senders of top-of-rack switch 1 and 4 first transmit mul-
ticast data to the aggregation switch. Then, the aggregation
switch has to transmit the same multicast data through four
different wired links for the four destinations. For the two
multicast trees, the total number of links used is 10 and the
total multicast data traffic is 10×1 Gbps = 10 Gbps. We can
see that the multicast trees with purely wired links result
in severe data redundancy. In Fig. 2(b), when the wireless
access points are considered, the multicast data of the first
multicast group can be transmitted by the access point of
rack 1 to that of rack 9. Then, the wireless access point
of rack 9 transmits data to the access point of rack 12. Thus,
rack 10, 11, and 12 can simultaneously receive the multicast
data. This multicast tree only uses the two wireless links. For
the second multicast group, since the access point of rack 5 is
interfered by the wireless transmission of the access point on
rack 1, the multicast data is selected to be transmitted by the
wired links and occupies five wired links. The total multicast
data traffic of the two multicast trees is 7×1 Gbps=7 Gbps.
Actually, we have a better option to build the multicast
trees as shown in Fig. 2(c). Interestingly, we can utilize the
wired links to avoid wireless interference such that more
FIGURE 2. An illustrative example for multicast tree construction in wireless data centers. (a) Multicast tree construction I. (b) Multicast
tree construction II. (c) Multicast tree construction III.

EMERGING TOPICS
FIGURE 3. An illustrative example for multicast tree maintenance in wireless data centers. (a) Multicast tree construction III.
(b) Multicast tree maintenance I. (c) Multicast tree maintenance II.
wireless access points can be simultaneously transmitted to
further reduce the data redundancy. The data of the first
multicast group can pass through the aggregation switch from
rack 1 to rack 12. Then, the wireless access point of rack 12
can relay the data to rack 9. The multicast tree for the first
multicast group is comprised of two wired links and one
wireless link. Then, the multicast data of the second multicast
group can be transmitted by the two wireless access points
on rack 4 and 8. The total data traffic for the two group
communications is (3 + 2)×1 Gbps = 5 Gbps.
2) MULTICAST TREE MAINTENANCE
The example in Fig. 3 depicts the multicast tree maintenance
problem, where the same system settings are used as that in
the example of the multicast tree construction. Moreover, in
this example, we adopt the two multicast trees constructed in
the example of multicast tree construction and consider that a
node of rack 5 joins multicast group 1, as shown in Fig. 3(a).
Then, we attempt to maintain the multicast trees such that the
node can receive the multicast data. As shown in Fig. 3(b),
the involved group (i.e., multicast group 1) intuitively uses
the wireless link to relay data from rack 9 to rack 5. However,
because the transmission interferes the wireless transmission
of the access point on rack 8, the multicast data of the vic-
tim group (i.e., group 2) is forced to be delivered via the
wired links. As a result, totally 4 Gbps redundant multicast
data traffic is increased. However, in this case, we should
use the wired link to transmit the data of group 1 instead.
The data can then pass through the aggregation switch from
rack 1 to rack 5 as shown in Fig. 3(c) and we only have 1 Gbps
more redundant data traffic under this solution. This example
demonstrates that the tree maintenance problem is important
and nontrivial in the minimization of the multicast data traffic
and has to be carefully addressed.
IV. THE MULTICAST TREE CONSTRUCTION
In this section, we prove the NP-hardness of the problem
by a reduction from the partition problem, which is known
to be NP-complete [23], and propose an efficient heuristic
algorithm to solve the multicast tree construction problem.
A. PROBLEM HARDNESS
Theorem 1: The multicast tree construction problem is
NP-hard.
Proof: The input instance of the partition problem is
a set of M integers, B = {b1, b2, . . . , bM }. The output is
YES if and only if B can be partitioned into two subsets
U and BU with the same sum, i.e., bm∈U bm =
bm∈U bm = 1
2 bm∈B bm.
Given an instance B of the partition problem, we explain
how to construct an instance G, CF
sisj
, CW
axay
, R, N of
our problem in polynomial time such that B can be evenly
partitioned if and only if there exist M multicast trees with
total data traffic 3
2 bm∈B bm. The construction is as follows:
We consider the wireless data center structure G shown
in Fig. 1. There are twelve racks, each of which is equipped
with a top-of-rack switch and a top-of-rack access point
(i.e., |VF | = 12 and |VW | = 12 ). The capacity of each wired
and wireless link is set at 1
2 bm∈B bm (i.e, CF
sisj
= CF
sjsi
=
CW
axay
= CW
ayax
= 1
2 bm∈B bm. There is a set of M multicast
groups (i.e., N = M). The multicast data of M multicast
groups is transmitted from rack 1 (source) to
rack 5 (destination) (i.e., νm = 1 and Dm = 5, ∀1 ≤ m ≤ M).
The data rate of multicast group m is set as Tm = bm,
∀1 ≤ m ≤ M.
To complete the proof, we show that two partitioned sub-
sets can be used to derive M multicast trees whose total
data traffic is 3
2 bm∈B bm, and vice versa. If there are two
partitioned subsets, each integer bm corresponds to the data
rate Tm required by multicast group m. A subset corresponds
to the data rate of the multicast groups transmitted by the two
wired links (i.e., the wired switch of rack 1 to the aggregation
switch and the aggregation to the wired switch of rack 5).
The other subset corresponds to the data rate of the other
multicast groups directly transmitted by the wireless link (i.e.,
the access point of rank 1 to the access point of rack 5).

EMERGING TOPICS
IN COMPUTING
Thus, the three links respectively transmit the data rate of
1
2 bm∈B bm and the total data traffic of M multicast trees
is 3
2 bm∈B bm. On the other hand, if the total data traffic
of M multicast trees is 3
2 bm∈B bm, the two wired links
and the wireless link have to respectively transmit the data
rate of 1
2 bm∈B bm. It implies that the set can be evenly
partitioned by assigning the corresponding integers into the
corresponding subset. The existence of a polynomial-time
algorithm for the partition problem implies the same for ours,
which completes the proof.
B. ALGORITHM DESCRIPTION
In this section, we propose an efficient algorithm for building
multicast trees, comprised of wired and wireless links, for
all multicast groups. The concept of this algorithm is to find
some wireless access points that can cover as more destina-
tions as possible to reduce the data redundancy of multicast
traffic. Then, we find shortest paths, comprised of wired and
wireless links, to connect each source with its destinations.
Moreover, in order to use as few number of links as possible,
for each shortest path, we will try to use wireless links first.
If the wireless link cannot support the data transmission,
we will utilize the wired link instead. Moreover, in order to
efficiently utilize each link capacity, we will give a higher
priority for the multicast group with a higher data rate to
construct the multicast tree.
The pseudo-code of the proposed algorithm is shown in
Algorithm 1. In Line 1, an indicator function lF (k, eF
sisj
) is
used to record whether wired link eF
sisj
is allocated for trans-
mitting the data of multicast group k, and is initialized as 0,
∀1 ≤ k ≤ N, eF
sisj
∈ EF . In Line 2, an indicator function
lW (k, eW
axay
) is used to record whether wireless link eW
axay
is
allocated to transmit the data of multicast group k, and is
initialized as 0, ∀1 ≤ k ≤ N, eW
axay
∈ EW . In Line 3,
a variable Pk, initialized as 0, is used record the priority of
multicast group k. If multicast group k has a higher value
of Pk, we have a higher priority to build a multicast tree for
the multicast group. In Line 4, a set ÊW
k is used to record
which wireless links can be adopted for delivering the traffic
of multicast group k. In Line 5, a set ˆSW
k is adopted to record
how many destinations of multicast group k can overhear
the multicast data transmitted by the access points of the
destinations (racks). In Line 6, a set ˆDk is used to register
which destinations of multicast group k can receive the data
and initialized as ∅.
Then, the algorithm starts to construct a multicast tree,
comprised of wireless and wired links, for each multicast
group (Lines 7-29). For each multicast group k, since the
directional antenna with narrow-beam is generally adopted
by wireless data centers, we let each wireless access point ax,
∀x ∈ Dk νk, attempt to transmit the data of multicast
group k to each wireless access point ay, ∀y ∈ Dk νk,
and compute how many destinations can receive the data
(Lines 7-13). In Lines 10-11, if access point ax of
rack x can transmit the data to access point ay of rack y
Algorithm 1 Multicast Tree Construction
Input: G, CF
sisj
, CW
axay
, R, N
Output: lF (k, eF
sisj
), lW (k, eW
axay
)
1: lF (k, eF
sisj
) ← 0, ∀1 ≤ k ≤ N, eF
sisj
∈ EF
2: lW (k, eW
axay
) ← 0, ∀1 ≤ k ≤ N, eW
axay
∈ EW
3: Pk ← 0, ∀1 ≤ k ≤ N
4: ÊW
k ← ∅, 1 ≤ k ≤ N
5: ˆSW
k ← ∅, ∀1 ≤ k ≤ N
6: ˆDk ← ∅, ∀1 ≤ k ≤ N
7: for k = 1 to N do
8: for all x ∈ (Dk νk) do
9: for all y ∈ (Dk νk) do
10: if eW
axay
∈ EW then
11: ˆSW
k ← ˆSW
k (SW
axay
Dk)
12: ÊW
k ← ÊW
k eW
axay
13: Pk ← Tk × |ˆSW
k |
14: Re-arrange the multicast group indexes by decreasing the
priority of Pk, ∀1 ≤ k ≤ N, such that P1 ≥ P2 · · · ≥ PN
16: Re-arrange the wireless link indexes by decreasing the
(SW
axay
Dk), ∀eW
axay
∈ ÊW
k
17: for all eW
axay
∈ ÊW
k do
18: if the access point capability constraint is satisfied
and |Dk Saxay | ≥ 2 and ˆDk Saxay = ∅ then
19: ˆDk ← ˆDk x
20: lW (k, eW
axay
) ← 1
21: SHORTEST-PATH(νk, x)
22: for all v ∈ Dk Saxay do
23: if the access point capability constraint is sat-
isfied then
24: ˆDk ← ˆDk v
25: else
26: Build a shortest path by wired links from νk
to v and set corresponding lF (k, eF
sisj
) as 1
27: ˆDk ← ˆDk v
28: if Dk ˆDk = ∅ then
29: SHORTEST-PATH(νk, Dk ˆDk)
30: return lW (k, eW
axay
) and lF (k, eF
sisj
), ∀ eW
axay
, eF
sisj
(i.e., eW
axay
∈ EW ), a set of destinations can receive
the data (i.e., SW
axay
Dk); and the set ˆSW
k is updated to
ˆSW
k (SW
axay
Dk). In Line 12, the wireless link eW
axay
that
can be used for transmitting the data of multicast group k is
added into the set ÊW
k . When all pairs of the access points of
destinations are tried out, the priority Pk of multicast group k
is set as Tk ×|ˆSW
k | (Line 13). That is, if more destinations can
overhear the data transmitted by the wireless access points
and the traffic of multicast group k has a higher data rate,
more data redundancy can be reduced. Thus, we give a higher
priority for the multicast group to build multicast tree and to
use wireless access points.

EMERGING TOPICS
After the priorities of all multicast groups are set, we
re-arrange the multicast group indexes by decreasing the
priority of Pk, ∀1≤k≤N, such that P1 ≥P2· · · ≥PN
(Line 14). Then, we start to build a multicast tree for each
multicast group and adopt the new index of multcast group,
i.e., multicast group k = 1 has the highest property P1
(Lines 15-29). For multicast group k, we re-arrange the wire-
less link indexes eW
axay
∈ ÊW
k by decreasing the (SW
axay
Dk)
in order to select the wireless links covering as more desti-
nations as possible (Line 16). Then, for each wireless link
eW
axay
∈ ÊW
k , we select access point ax transmitting data to
access point ay if the following three conditions are met
(Lines 17-18): 1) the access point can meet its capability
constraint; 2) at least two destinations can simultaneously
receive the multicast data (i.e., |Dk Saxay | ≥ 2); and
3) each destination of multicast group k cannot receive the
same multicast data from more than one link in order to
meet the tree properties (i.e., ˆDk Saxay = ∅). If the link
is adopted, we add destination (rack) x, which can receive
data, to the registered destination set ˆDk (i.e., ˆDk = ˆDk x)
(Line 19) and the indicator function lW (k, eW
axay
) is set as 1
accordingly (Line 20). Although the wireless link eW
axay
is
adopted and can transmit data to some destinations, access
point ax does not have a path to receive the multicast traffic
from sender νk. Then, we find a shortest path, comprised
of wired and wireless links, for the given pair of source νk
and access point ax of rack x. Whenever Procedure
SHORTEST-PATH() is invoked, it attempts to find a shortest
path from source νk of multicast group k to destination x
through as few links as possible (Line 21). For the path, we
try to use wireless links first. If the wireless links do not
satisfy the access point capability constraint, we adopt wired
links instead. Then, the corresponding indicator functions
lW (k, eW
˜x˜y) and lF (k, eF
˜i˜j
) are set as 1.
In Lines 22-27, although the access point av of the
destination rack v can overhear the wireless transmission
(i.e., v ∈ Dk Saxay ), it may not have enough capability to
receive the data. Therefore, if the access point has capability
to receive the data, we directly add the destination of rack v
to the registered destination set ˆDk (Line 24). Otherwise,
we build a shortest path by wired links from sender νk to
destination v and set corresponding lF (k, eF
sisj
) as 1 (Line 26).
The destination of rack v is also added to the registered
destination set ˆDk (Line 27). Finally, if there are some remain-
ing destinations that have no path to receive multicast data
(i.e., Dk ˆDk = ∅), we use Procedure SHORTEST-PATH()
to find a shortest path for each remaining destination of
multicast group k (Lines 28-29). Finally, we return a multicast
tree, comprised of wireless and wired links, for each multicast
group (Line 30).
Theorem 2: The time complexity of Algorithm 1 is
O(N ˜D( ˜Eω + ˜D)). ˜D = max
∀ k
|Dk|; ˜E = max(|EW |, |EF |). ω is
the running time of the shortest path algorithm.
Proof: The initialization process requires O(N ˜E) time.
For each multicast group k, a priority Pk is computed only
once and can be done in O( ˜D2). Thus, for N multicast groups,
the algorithm takes O(N ˜D2) time. For building a multicast
tree of group k, there are at most ˜D destinations and ˜E links;
and Procedure SHORTEST-PATH() is used only once for
each destination. Building multicast trees for N multicast
groups takes O(N ˜E ˜Dω). Thus, the time complexity
of Algorithm 1 is O(N ˜D( ˜Eω + ˜D)).
V. THE MULTICAST TREE MAINTENANCE
In this section, we also show that the problem is NP-hard,
and respectively propose an efficient heuristic algorithm to
maintain the multicast trees for nodes joining and leaving.
A. PROBLEM HARDNESS
Theorem 3: The multicast tree maintenance problem is
NP-hard.
Proof: This theorem can be proved in a similar way to
Theorem 1. The input instance in Theorem 1 is reused in this
theorem. We describe how to construct the additional inputs
of the multicast tree maintenance problem (i.e., Jm and Lm).
Any M multicast trees have been constructed in the multicast
tree construction problem and the capacity of each wired
and wireless link is exhausted. Now, we consider that
rack 5 and rack 9 are additionally equipped with one wired
switch and connected with two wired links so that the two
racks can transmit data directly. Each multicast group m has
a node in rack 9 requesting to join (i.e., |Jm| = 1) and does
not have any node requesting to leave (i.e., |Lm| = 0). The
multicast data of M multicast groups also has to transmit
to rack 9 (destination) from rack 5 (i.e., Dm = Dm 9,
∀1 ≤ m ≤ M).
To complete the proof, we show that two partitioned
subsets can be used to derive the tree maintenance for M
multicast trees whose the increased data traffic is bm∈B bm,
and vice versa. If there are two partitioned subsets, each
integer bm corresponds to the data rate Tm required by mul-
ticast group m. A subset corresponds to the data rate of
the multicast groups. The data of the multicast groups is
directly transmitted via one wired link. The other subset
corresponds to the data rate of the other multicast groups,
which should be transmitted by the other wired link. Since
each wired link transmits the data rate of 1
2 bm∈B bm, the
totally increased data traffic is bm∈B bm. On the other hand,
if the totally increased data traffic of M multicast trees is
bm∈B bm, each wired link has to respectively transmit the
data rate of 1
2 bm∈B bm. It implies that the set can be evenly
partitioned by assigning the corresponding integers into the
corresponding subset. The existence of a polynomial-time
algorithm for the partition problem implies the same for ours,
which completes the proof.
B. ALGORITHM DESCRIPTION FOR NODE JOINING
This section propose a polynomial time algorithm to deal
with the multicast tree maintenance problem for node joining.
When there are nodes requesting to join multicast groups,
how to maintain each multicast tree is a complicated problem.

EMERGING TOPICS
IN COMPUTING
Algorithm 2 Node Joining
Input: G, CF
sisj
, CW
axay
, Jk, N, lF (k, eF
sisj
), lW (k, eW
axay
), R
1: ˆlF (k, eF
axay
) ← lW (k, eW
axay
), ∀1 ≤ k ≤ N, eF
sisj
∈ EF
2: ˆlF (k, eF
sisj
) ← lF (k, eF
sisj
), ∀1 ≤ k ≤ N, eW
axay
∈ EW
4: for all jk ∈ Jk do
5: Flag = false
6: for all {eW
axay
|lW (k, eW
axay
) = 1} do
7: if jk ∈ Saxay then
8: Flag = true
9: break
10: if Flag = false then
11: for all {eW
axay
|lW (k, eW
axay
) = 1} do
12: if eW
axajk
∈ EW then
13: CHECK-CAPABILITY(eW
axay
, eW
axajk
)
14: Flag = true
15: break
16: else if eW
ajk
ay
∈ EW then
17: CHECK-CAPABILITY(eW
axay
, eW
ajk
ay
)
18: Flag = true
19: break
20: if Flag = false then
21: SHORTEST-PATH(νk, jk)
22: return ˆlW (k, eW
axay
) and ˆlF (k, eF
sisj
), ∀ eW
axay
, eF
sisj
Specifically, when a node joins a multicast group in a rack and
we would like to transmit data to the rack via a wireless link,
multiple wireless links of the existed groups may interfere
the access point of the rack. Under the limited capacity of the
access point, some groups have to change their tree structures
as the victim groups. However, each victim group has
tremendous choices to select other substitute paths via
wired and/or wireless transmissions. With the considera-
tion of the feasibility, we are impossible to process all the
possible selections in our algorithm. To tackle this problem,
we design a procedure, named collision procedure, by observ-
ing the structure of the wireless data centers to sieve out an
efficient substitute path from all the possible selections. In the
procedure, we build the substitute path for each victim group
and avoid the chain reaction, when the victim groups have to
change their tree structures.
The pseudo-code of the algorithm is shown in Algorithm 2.
In Lines 1-2, the new indicator function ˆlW (k, eW
axay
) and
ˆlF (k, eW
sisj
) are initially set as the wired and wireless links
of the multicast trees constructed in Algorithm 1. Then, the
algorithm starts to reconstruct multicast trees for the joining
requests (Lines 3-21). For rack jk, ‘‘Flag’’, initialled as false,
is used to indicate that rack jk can receive the multicast
data of group k or not (Line 5). Then, we check whether
the rack is covered by a wireless link of itself tree structure
and directly receive the data. It implies the tree structure
of group k does not require to be changed and Flag is set
as true (Lines 6-9). Otherwise, we attempt to adjust the
tree such that the rack can receive the data (Lines 10-19).
We try to lengthen each wireless link which is already used by
group k and there are two possible directions (Lines 11-19).
For each used wireless link eW
axay
of group k, the first case
for the lengthened direction is rack jk as the new desti-
nation in the right hand side of the original destination
(i.e, rack y) and the wireless link eW
axay
is changed as eW
axajk
(Lines 12-13). The other case is rack jk as the new sender
in the left hand side of the original sender (i.e., rack x) and
the wireless link eW
axay
is changed as eW
ajk
ay
(Lines 16-17).
Since the lengthened wireless link will interfere more access
points on the racks such that their capacity may not be suf-
ficient (abbreviated as collision racks), it implies that many
wireless links of other groups, which pass through the col-
lision racks, will be affected as well. Therefore, Procedure
CHECK-CAPABILITY() is involved to check the capacity
of each access point, covered by the lengthened wireless, link
and determine which groups should be the victim groups to
change their tree structures (Line 13 or 17). If we cannot
transmit data to rack jk by lengthening a wireless link from
the original multicast tree, we build a shortest path with
wired links to transmit data to rack jk by involving Procedure
SHORTEST-PATH() (Lines 20-21).
Procedure CHECK-CAPABILITY(eW
axay
, eW
auat
)
1: for all a ∈ Sauat do
2: if the capability constraint of access point a is not
satisfied then
3: ˆBk ← ˆBk a
4: if | ˆBk| = ∅ then
5: ˆlW (k, eW
axay
) ← 0 and ˆlW (k, eW
auat
) ← 1
6: else
7: COLLISION( ˆBk)
Procedure CHECK-CAPABILITY() takes original
wireless link eW
axay
and lengthened wireless link eW
auat
as
inputs. When lengthened wireless link eW
auat
is used, each
access point a ∈ Sauat will be interfered. If the capability
constraint of an access point a ∈ Sauat is not satisfied,
we add the access point of the rack to set ˆBk (Lines 1-3).
If the capacity constraint of all the access points are satisfied
(i.e., | ˆBk| = 0), lengthened wireless link eW
auat
is adopted
(i.e., ˆlW (k, eW
auat
) = 1) and original wireless link eW
axay
is
released (i.e., ˆlW (k, eW
axay
) = 0) (Lines 4-5). Otherwise, we
trigger Procedure COLLISION() to determine which groups,
with wireless links passing through the collision rack, should
be the victim groups to change their tree structures.
Procedure COLLISION() (see next page) takes the set of
collision racks ˆBk as input. This procedure is to determine
which groups should be the victim groups to change their tree
structure. If there is only one collision rack (i.e., |ˆBk| = 1),
we calculate a priority ˆPg, initialized as 0, for each multicast
group g ∈ MˆBk
(Line 1), where MˆBk
is the set of groups
which has a wireless link passing through the access point
of the collision rack (Lines 1-7). The higher the priority,

EMERGING TOPICS
Procedure COLLISION(ˆBk)
1: ˆPg ← 0, ∀1 ≤ g ≤ N
2: if |ˆBk| = 1 then
3: for all g ∈ MˆBk
do
4: for all {eW
axay
|ˆlW (g, eW
axay
) = 1} do
5: if ˆBk ∈ Saxay then
6: ˆPg = {HOPPING()−Tg }
priority of ˆPg
8: for all g ∈ MˆBk
do
9: if ˆPg > 0 and the capacity constraint of the access
point ˆBk is not satisfied then
10: set the corresponding wireless and wired link
indicator function as 1
11: else
12: Build a shortest path by wired links from νk to jk and
set corresponding ˆlF (k, eF
sisj
) as 1
the more the increased data redundancy. Then, according
to the priorities, the groups with higher priorities will still
use the original wireless link. Until the capacity of the access
point is not enough, the other groups with lower priorities will
be the victims groups to change their paths. Otherwise, if the
collision racks are more than one, with the consideration of
the feasibility for computation complexity, we will use wired
links to connect the joining node in the rack jk. (Lines 11-12).
Now, we explain how to calculate priority Pg for group g
(Line 6). If the wireless link of group g, passing through the
collision rack, is released, we have to rebuild a path instead
of the released wireless link. For finding a substitute path,
we are impossible to search all the possible paths. Thus, we
observe the structure of the wireless data center to find an
efficient substitute path comprised of wired and wireless links
as shown in Fig. 4, when the group should be the victim group
to change its tree structure.
FIGURE 4. An illustration for Procedure COLLISION(). (a) The
original wireless links. (b) Group 1 is the victim group when
a node joins group 2 in rack 3.
Fig. 4(a) shows a wireless link of group 1 and 3 when
no any node requests to join. When a node requests to
join group 2 in rack 3, a wireless link is lengthened to
rack 3 for transmitting the data to the node such that the
capacity of the access point on rack 3 is not enough. Let
group 1 be the victim group. Then, we rebuild a sub-
stitute path, comprised of two wireless links and three
wired links, for the destinations of group 1 in order to
avoid the interference on the access point on rack 3, as
shown in Fig. 4(b). Thus, for the new path of group 1,
the priority (increased data redundancy) P1 is 5T1 - T1,
where 5T1 is the data redundancy of group 1 under the new
substitute path in Fig. 4(b) and T1 is the data redundancy
of group 1 under the original wireless link in Fig. 4(a).
Priority Pg will be calculated by Function Hopping().
Consequently, groups with low Pg will be the victim groups
in order to reduce the increased data redundancy and we set
the corresponding wired and wireless link indicator function
as 1 for the new substitute path (Lines 8-10).
O(N ˜J(˜S ˜E + ˜M ˜E2 + ω)). ˜J = max
∀k
|Jk|; ˜S = max
∀axay
(|Saxay |);
˜M = max
∀k
|MˆBk
|.
Proof: There are at most N groups (Line 3 of
Algorithm 2). For each multicast group k, at most ˜J racks
have to receive data of group k (Line 4 of Algorithm 2).
For each rack which has nodes joining to group k, we try
to lengthen a wireless link selected from at most ˜E wireless
links to transmit data to the rack (Lines 6-19 of Algorithm 2).
If we can lengthen a wireless link to transmit data to the
rack, Procedure CHECK-CAPACITY() and COLLISION()
will be involved (Lines 10-19 of Algorithm 2). Procedure
CHECK-CAPACITY() will check the capacity of the access
points covered by the lengthened wireless link and takes
O(˜S) time (Lines 1-3 of Procedure CHECK-CAPACITY).
Procedure COLLISION() will compute a priority for each
group which has a wireless link passing through the collision
rack. Since there are at most ˜M groups each of which has
at most ˜E wireless links to be checked, this procedure takes
O( ˜M ˜E) time (Lines 3-6 of Procedure COLLISION). Since
there are at most ˜E wireless links, searching wireless links
for N groups, each of which has nodes joining in at most ˜J
racks, takes O(N ˜J(˜S ˜E + ˜M ˜E2) time. Otherwise, if no any
wireless link is suitable for transmitting data to the rack, wired
links via involving SHORTEST-PATH() which takes O(ω)
time, are instead. Thus, the time complexity of Algorithm 2
is O(N ˜J(˜S ˜E + ˜M ˜E2 + ω) (Lines 3-21 of Algorithm 2).
C. ALGORITHM DESCRIPTION FOR NODE LEAVING
In this section, we propose a polynomial time algorithm to
maintain the multicast trees for node leaving. The concept of
the algorithm design is to retrieve unused wireless links and
reassign the wireless resource to other groups. When a node
leaves a multicast group, the wireless resource on a rack could
be released and the released resource can be used for other
multicast groups which use wired links to transmit data to the
rack. Since multiple groups on the rack have to compete the
wireless resource, we have to determine which groups should

EMERGING TOPICS
IN COMPUTING
Algorithm 3 Node Leaving
Input G, CF
sisj
, CW
axay
, Lk, N, lF (k, eF
sisj
), lW (k, eW
axay
), R
1: ˆlF (k, eF
sisj
) ← ˆlW (k, eW
axay
), ∀1 ≤ k ≤ N, eF
sisj
∈ EF
2: ˆlF (k, eF
sisj
) ← lF (k, eF
sisj
), ∀1 ≤ k ≤ N, eW
axay
∈ EW
4: for all lk ∈ Lk do
5: for all {eW
axay
|lW (k, eW
axay
) = 1} do
6: if lk ∈ Saxay and Dk Saxay = ∅ and
LeafNode(alk ) = true then
7: lW (k, eW
axay
) ← 0
8: REALLOCATION(Saxay )
9: PRUNE(ax, Dk)
10: break
11: return ˆlW (k, eW
axay
) and ˆlF (k, eF
sisj
), ∀ eW
axay
∈ EW , eF
sisj
∈
EF
use the wireless resource instead of wired links and how
to use. Moreover, when there are nodes requesting to join,
Algorithm 2 may generate some victim groups and rebuilds
a substitute path for the victim groups. We also address
how to recover an efficient path from the substitute path.
To deal with the above problems, we respectively design a
procedure prune and reallocation to retrieve unused wireless
links and reassign the released wireless resource to other
groups.
The pseudo-code of the proposed algorithm for node leav-
ing is shown in Algorithm 3. In Lines 1-2, the new indicator
functions ˆlW (k, eW
axay
) and ˆlF (k, eW
sisj
) are the same as the
Lines 1-2 of Algorithm 2. For each leaving node lk ∈ Lk of
group k, we check each wireless link used by group k whether
can be retrieved if there are nodes of group k requesting
to leave. The resource of a wireless link can be released
when the following three conditions are met (Lines 4-6).
1) The leaving node is covered by the transmission range of
the wireless link. 2) The transmission range of the wireless
link does not cover any other destination. 3) The leaving
node is a leaf node in the tree, because when the leaving
node is not a leaf node, the wireless link may be used to
relay data and cannot be released. If the resource of wireless
link eW
axay
can be released, we retrieve the wireless link and
set the indicator function lW (k, eW
axay
) as 0 (Line 7). Since
the wireless link of group k is retrieved, the access points
on the racks (abbreviated as ‘‘involved racks’’), originally
interfered by the wireless link, get free capacity Tk. Thus,
Procedure REALLOCATION() is designed to reallocate the
released wireless resource to other groups which use wired
links to transmit data to the involved racks (i.e., Saxay ) and
determine which groups should use the released wireless
resource instead of the wired links (Line 8). Because the
leaving node is a leaf node of the tree, a path may include
multiple wireless links to relay data to the leaf node from the
root. Thus, we have chance to retrieve more wireless links of
the path. Hence, Procedure PRUNE() tries to revoke more
wireless links to further reduce data redundancy (Line 9).
Finally, we return the two indicator functions
(Line 11).
Procedure REALLOCATION(Saxay )
1: ˆPg ← 0, ∀1 ≤ g ≤ N
2: for all z ∈ Saxay do
3: for all g ∈ Hz do
4: LeftLink = false
5: RightLink = false
6: for all {eW
axay
|ˆlW (g, eW
axay
) = 1} do
7: if ˆlW (g, eW
axaz
) = 1 and all access points capability
are satisfied then
8: LeftLink = true
9: else if ˆlW (g, eW
azay
) = 1 and all access points capa-
bility are satisfied then
10: RightLink = true
11: if LeftLink = true and RightLink = true and the two
wireless links can be combined then
12: ˆPg = WIRED-COST(ˆl(g, eF
sisj
)) + Tg
13: else if LeftLink = true or RightLink = true then
14: ˆPg = WIRED-COST(ˆl(g, eF
sisj
))
priority of ˆPg
16: for all g = 1 to |Hz| do
17: if ˆPg > 0 and all access points capability constraint
are satisfied then
18: set the corresponding indicator function of wire-
less links as 1 and of wired links as 0
Procedure REALLOCATION() takes Saxay as input to
reallocate wireless resource of each access point on each
involved rack in Saxay . In Line 1, variable ˆPg, initialized as 0,
is used to record a priority value for each multicast group. The
value of ˆPg means an amount of the data redundancy used
by group g. For each involved rack z ∈ Saxay , there is a set
of groups Hz which has a destination (node) in rack z and
uses a wired link to transmit data to rack z (Line 2). For each
group g ∈ Hz, we attempt to lengthen an existed wireless link
instead of the wired link to transmit data to the destination
of group g in rack z (Lines 3-14). To lengthen each wireless
link eW
axay
which is already used by group k, there are two
possible directions. The first one is that access point ax can
transmit data to rack z and rack z can be the new destination
in the right hand side of rack y (i.e., ˆlW (g, eW
axaz
) = 1). If the
wireless link can transmit data to rack z via lengthening, flag
LeftLink is set as true (Lines 7-8). Similarly, the other one is
that access point az, as the new sender in the left hand side
of rack x, can transmit data to rack y (i.e., ˆlW (g, eW
azay
) = 1).
If the access point on rack z can transmit data to rack y by
lengthening the wireless link, flag RightLink is set as true
(Lines 9-10).
Now, we calculate priority ˆPg for group g to record an
amount of data redundancy that can be reduced. If the two
flags are true and one of the two wireless links can cover

EMERGING TOPICS
all the destinations that the other wireless link can cover,
it means that the two wireless links can combine as one
wireless link. The priority of group g is set as WIRED-
COST()+Tg (Lines 11-12), where WIRED-COST() will
return that an amount of the wired link data rate used by
the group g is retrieved and the value of Tg represents the
retrieved wireless resource. Otherwise, if flag LeftLink or
RightLink is set as true, the priority of group g is set as
WIRED-COST() because only wired links can be retrieved
(Lines 13-14). After each involved multicast group has a
priority value, we re-arrange the involved group indexes by
decreasing the priority of ˆPg (Line 15). Then, according to
the priority value, the groups with higher priority will use
the wireless resource first instead of the used wired links to
reduce the data redundancy until the capacity of the access
point on rack z is insufficient. Finally, we set the correspond-
ing indicator function of wireless links as 1 and of wired links
as 0 (Lines 16-18).
We use the same example shown in Fig. 4 to explain how to
lengthen wireless links and to calculate a priority for group 1,
when the node in rack 3 leaves group 2. For the destination of
group 1 in rack 3, the first direction to lengthen a wireless link
is that the access point on rack 1 can transmit data to rack 3.
The other direction is that the access point on rack 3 as the
new sender can transmit data to the access point on rack 6.
Since the two wireless links can cover the same destinations,
they can combine as one wireless link. Thus, the path of
group 1 shown in Fig. 4(b) can recover to the original wireless
link of group 1 shown in Fig. 4(a). Thus, group 1 only uses
one wireless link instead of the five links. In this case, one
wireless link and three wired links are retrieved.
WIRED-COST() returns 3T1 and ˆP1 is 4T1.
Procedure PRUNE(ay, Dk)
1: ax ← PARENT(ay)
2: if LeafNode(ay) = ∅ and Dk Saxay = ∅ then
3: lW (k, eW
axay
) ← 0
4: REALLOCATION(Saxay )
5: PRUNE(ax)
In Procedure PRUNE, we try to retrieve more wireless
links of a path transmitting data to access point ay. This
is because a multicast tree may adopt many wireless links
to relay data to only one destination. In Line 1, we use
PARENT() to find the parent node of access point ay.
In order to ensure the connectivity of multicast tree, we
retrieve the wireless link if the access point is a leaf node and
the wireless link does not cover any other destination (Line 2).
Then, we retrieve the wireless link and set the indicator
function as 0 (Line 3). Then, since the resource of the wireless
link is released, we trigger Procedure REALLOCATION()
to reassign the wireless resource to other multicast groups
which use wired links to transmit their multicast data (Line 4).
In Line 5, we try to retrieve one more wireless link of the
tree until the wireless link of next parent node cannot be
revoked.
O(N ˜L ˜E2 ˜S ˜Hτ). ˜L = max
∀k
|Lk|; ˜H = max
∀z
(|Hz|);
τ = max
∀k
(TreeDepth(k)).
Proof: There are at most N groups (Line 3 of
Algorithm 3). For each multicast group k, there are at most
number of leaving nodes ˜L (Line 4 of Algorithm 3). For
each leaving node, we attempt to retrieve a wireless link
from at most ˜E wireless links (Line 5 of Algorithm 3). If a
wireless link can be revoked, we reallocate the released wire-
less resource by involving Procedure REALLOCATION()
and PRUNE() (Lines 6-9 of Algorithm 3). In Procedure
REALLOCATION(), the number of the involved racks,
covered by a wireless link, is at most ˜S. For an involved
rack, there are at most ˜H groups with a destination in the
involved rack. For a group, we have to check at most ˜E
wireless links and calculate a priority (Lines 2-14 of
Procedure REALLOCATION()). The procedure takes
O(˜S ˜H ˜E) time. In Procedure PRUNE(), if it retrieves a wire-
less link, Procedure REALLOCATION() will be involved
once. Since the depth of a tree is at most τ, Procedure
REALLOCATION() will be involved at most τ times. Thus,
the complexity of Algorithm 3 is O(N ˜L ˜E2 ˜S ˜Hτ).
VI. PERFORMANCE EVALUATION
A. SIMULATION SETUPS
In this section, we develop a simulation model based
on a realistic wireless data center topology, where the
hierarchical topology is used according to the deployment of
Microsoft [6], to evaluate our proposed algorithms. In the net-
work architecture, there are 160 top-of-racks, each of which
has one wired switch and one 60GHz wireless access point
with a directional narrow-beam antenna. The real measure-
ment results from Microsoft have indicated that two parallel
60GHz wireless links are interfered with each other when the
distance of the two links is smaller than 22 inches. Note that
the width of a rack is about 24 inches. By the geometric-based
interference model and the deployment of wireless access
points, the transmission range of each wireless link and its
interference can be accordingly derived, and an example is
shown in Fig. 5.
FIGURE 5. An illustration for understanding the range of
wireless interference in wireless data centers.

EMERGING TOPICS
IN COMPUTING
The maximal capacity of each link is set as 1Gbps when
background traffic is not considered. However, to investigate
the impacts of background traffic, the available capacity of
each link is randomly assigned from 300 Mbps to 1000 Mbps
if background traffic is heavy in data centers [24].
On the other hand, for the case of light background traffic,
the available capacity of each link is randomly set from
700 Mbps to 1000 Mbps. Moreover, the number of multi-
cast groups in our experiments varies from 50 to 250 [13].
For each multicast group, one source and some destinations
are randomly selected from 160 top-of-racks. To determine
the number of destinations in a multicast group, we consider
two different distributions [19]. The first one is uniform distri-
bution with the range from 3 to 160. The other one is power-
law distribution, which generates more small groups in the
data center. The data rate for each multicast group is set based
on the real data flows in a data center [25], and it is selected
as one of the following six data rates, 1, 10, 100, 1000, 10000,
100000kbps, with the corresponding probabilities 0.1, 0.3,
0.2, 0.2, 0.15, and 0.05.
We compared our proposed algorithm with other
algorithms for tree construction and maintenance. For tree
construction, our Efficient Wireless Data Center Multicast
Tree (EWDCMT) approach is compared with two algorithms.
The first algorithm, denoted as steiner-tree, was designed
for wired data center networks; the algorithm obtains an
optimal multicast tree for each multicast group regardless
of the link capacity constraint of each wired link. In order
to have a fair comparison, we relax the constraint for
steiner-tree. Note that relaxing the constraint is beneficial
for the performance of steiner-tree. The second algorithm,
represented as shortest-path-tree, was designed as a baseline.
The algorithm builds shortest-path trees with the considera-
tion of wired and wireless links in wireless data centers. For
each shortest path tree, the algorithm uses wireless links first.
Until the available capacity of an access point is exhausted,
the algorithm adopts wired links instead. The performance
metric is the total amount of transmitted data traffic for all
multicast groups.
For tree maintenance, EWTM-J and EWTM-L were
proposed to deal with the cases for node joining and leaving
a multicast group. We adopt three algorithms for the per-
formance comparison. EWDCMT is considered as the lower
bound for the tree maintenance problem. A random approach,
denoted by Random, randomly chooses wired or wireless
links to modify an original multicast tree when receiver
joins the multicast group. The third algorithm, represented
as Retrieval, revokes the resource of a wireless link when
the transmission range of the wireless link does not cover
any destination and the leaving node is a leaf node. In this
experiment, the numbers of multicast groups are 50 and 250,
where the size for each group is initially generated by the
power-law and the uniform distributions. Then, the number
of joining or leaving nodes varies from 100 to 1000, and each
node is randomly and subsequently added/removed into/from
one of the groups. The performance metric used for tree
maintenance is the amount of increased/decreased multicast
traffic when the receivers join/leave multicast groups. Finally,
we have compared the three algorithms in terms of the
execution time when 500 nodes join/leave multicast groups.
The experiment is conducted by a desktop computer with
Intel CPU I7-3770 3.4GHz and 16GB RAM.
The simulation parameters are listed in Table 2.
We measure the simulation results from averaging the results
of 500 independent simulations.
TABLE 2. Parameter settings.
B. SIMULATION RESULTS
1) MULTICAST TREE CONSTRUCTION
Fig. 6 shows the impacts of the number of multicast groups
under different group size distributions on the total multi-
cast data traffic. As shown in the figure, the total multicast
data traffic increases when the number of multicast groups
increases for the three algorithms. The figures intuitively
show that more multicast groups increase more multicast
data traffic and use more network resources. However, our
proposed algorithm can efficiently reduce the total multi-
cast data traffic against steiner tree and shortest path tree.
Comparing Fig. 6(a) with Fig. 6(b), the performance of
shortest path tree is close to that of steiner tree when we
consider the uniform group size distribution. The reason is
that each multicast group with the uniform group size has
a relatively large number of members (destinations). Each
member is randomly placed in the wireless data center, so that
shortest path tree may rapidly exhaust the capacity of each
wireless link. Thus, wired links are used instead and the per-
formance of shortest path tree is similar to that of steiner tree.
In contrast, EWDCMT significantly reduces more data redun-
dancy, compared with steiner tree and shortest path tree,
FIGURE 6. Impacts of the number of multicast groups under
(a) the uniform group size distribution and (b) the power-law
group size distribution on the total multicast data traffic.

EMERGING TOPICS
under the uniform group size distribution than under the
power-law group size distribution. This is because our
algorithm efficiently uses each wireless link and finds each
access point that transmits data to as more destinations as
possible. When each multicast group has more destinations,
our algorithm efficiently utilizes the broadcast advantage of
wireless medium for multicast transmissions and evidently
reduces the data redundancy of multicast traffic. The sim-
ulation results show that EWDCMT reduces the total data
traffic, compared with steiner-tree and shortest path tree,
from 39% to 66% under the uniform group size shown
in Fig. 6(a) and from 48% to 55% under the power-law group
size distribution.
Fig. 7 shows the impacts of different background traffic
levels on the total multicast data traffic. As we can see in
this figure, the total multicast data traffic is higher, when the
background traffic load is higher, under shortest path tree and
EWDCMT. The reason is that when the background traffic
increases, those efficient wireless links for each multicast
group may not afford to satisfy the increased traffic demand.
In order to avoid over-utilization, the two algorithms must use
other inefficient wireless/wired links for building multicast
trees such that data redundancy can be increased. This also
explains why the performance of EWDCMT is close to those
of shortest path tree and steiner-tree when the background
traffic is heavy. On the other hand, the background traffic
level does not have any impact for steiner-tree, since
steiner-tree does not consider the link capacity constraint of
wired links. Comparing Fig. 7(a) with Fig. 7(b), the result is
similar to that in Fig. 6. The performance of our proposed
algorithm, compared with steiner-tree and shortest path tree,
is more efficient for reducing total multicast data traffic under
the uniform group size distribution, shown in 7(a), than under
the power-law group size distribution, shown in 7(b). The
simulation results show that EWDCMT outperforms steiner-
tree and shortest path tree. The reduction is about 56% under
the uniform group size distribution and is about 52% under
the power-law group size distribution.
FIGURE 7. Impacts of the number of multicast groups for (a) the
uniform group size distribution and (b) the power-law group
size distribution on the total multicast data traffic under
50 multicast groups.
In addition to the topology used by Microsoft and the
synthetic input of data rates for multicast traffic, we collected
real traces of MepReduce in Chunghwa Telecom data center
to evaluate the performance of EWDCMT. In this data
center, there are six top-of-racks and 120 servers as a cluster
for cooperating computation, and the six top-of-racks are
arranged in a straight line. Based on the real traces,
the corresponding data rates can be parsed. Fig. 8 shows
the impact of the number of multicast groups on the total
multicast data traffic based on the real traces. The result
is consistent with the results following the settings by
Microsoft. In this figure, we found that our proposed
algorithm can save at most 86% of the total multicast data
traffic in comparison with steiner-tree and shortest-path-tree,
which indicates that our proposed algorithm efficiently uses
network bandwidth for multicast transmissions to reduce
unnecessary multicast traffic in a realistic environment.
FIGURE 8. Impact of the number of multicast groups on the total
multicast data traffic by the real traces of MapReduce from
Chunghwa Telecom.
2) MULTICAST TREE MAINTENANCE
Fig. 9 shows the impacts of the number of joining nodes
with power-law distribution on the amount of the increased
multicast traffic when there are 50 and 250 multicast groups.
We observe that the amount of the multicast traffic increases
as the number of joining nodes increases for Random,
EWDCMT and EWTM-J. This result can be expected because
more joining nodes imply more traffic requests. Compared
with Random, our proposed algorithm EWTM-J can save
more unnecessary multicast traffic, because EWTM-J can
efficiently maintain the used wireless links or can find substi-
tute paths for the victims groups. Moreover, the performance
of our algorithm is close to that of EWDCMT. By comparing
Fig. 9(a) with Fig. 9(b), the performance of EWDCMT and
FIGURE 9. Impacts of the number of joining nodes with the
power-law group size distribution on the amount of the
increased multicast traffic under (a) 50 multicast groups
and (b) 250 multicast groups.

EMERGING TOPICS
IN COMPUTING
EWTM-J is closer to Random under 250 groups than under
50 groups. This is because when the group size increases,
more groups have to compete wireless resources and be the
victim groups to use wired links. The simulation results show
that compared with Random, EWTM-J can reduce the amount
of the increased multicast traffic to 53% under the case
of 50 multicast groups. Moreover, EWTM-J generates the
amount of the multicast traffic at most 26% more
than EWDCMT.
FIGURE 10. Impacts of the number of joining nodes with uniform
group size distribution on the amount of the increased
multicast traffic under (a) 50 multicast groups and
(b) 250 multicast groups.
Fig. 10 shows the impacts of the number of joining nodes
with uniform distribution on the amount of the increased
multicast traffic for 50 and 250 multicast groups. As shown
in Fig. 10(a), the result is similar to that in Fig. 9(a) when
the group size is 50. On the other hand, when the group size
is 250, the performance of the three algorithms is similar as
shown in Fig. 10(b). This phenomenon is due to that the three
algorithms will exhaust wireless resources under 250 groups
with uniform distribution and wired links are unavoidably
used.
Fig. 11 shows the impacts of the number of leaving nodes
with power-law distribution on the amount of the increased
multicast traffic under 50 and 250 multicast groups. The
amount of the multicast traffic decreases when the number
of leaving nodes increases for all of the three algorithms.
The reason is that more wired and wireless resources are
released for optimizing the resource allocation for the remain-
ing nodes when there are more leaving nodes. As shown
FIGURE 11. Impacts of the number of leaving nodes with
power-law group size distribution on the amount of the
in Fig. 11(a), the decrease on the amount of the multicast
traffic is more evident under EWTM-L than under Retrieval.
This is because our algorithm tries to revoke all of the unused
links in the transmission path for a group and reallocate the
resources to other groups, while Retrieval only considers the
wireless link used by the leaving nodes. Comparing Fig. 11(a)
with Fig. 11(b), EWTM-L can release more resources under
50 groups than under 250 groups. This phenomenon is that
when the number of groups is fewer, the leaving nodes are
very likely to belong to the same group such that more
resource can be released and reallocated to other groups.
On the other hand, when there are more number of groups,
the leaving nodes are probably distributed to different groups
such that the wireless resources for the leaving nodes cannot
be completely released.
Fig. 12 shows the impacts of the number of leaving nodes
with uniform distribution on the amount of the increased
multicast traffic under 50 and 250 multicast groups. As shown
in Fig. 12(a) and 12(b), under the uniform distribution, the
decreased multicast traffic is not evident for EWTM-L. The
reason is similar to that for Fig. 11(b). EWTM-L only real-
locates the released wireless resource. When the resource
is occupied by few nodes, our proposed algorithm does not
have a chance to reallocate the wireless resources. In contrast,
EWDCMT can reallocate all the wired and wireless resource
for all groups. When there are more leaving nodes, EWDCMT
can release more bandwidth as expected. Compared with
Fig. 12(a) and Fig. 12(b), EWDCMT can reduce more data
traffic under 50 groups than under 250 groups. This is because
when there are more nodes in a group, EWDCMT can more
efficiently reallocate wireless transmissions to reduce data
redundancy.
FIGURE 12. Impacts of the number of leaving nodes with the
uniform group size distribution on the amount of the
Figs. 13 and 14 respectively show the impacts of the
number of groups on the average running time required for
each algorithm. From these figures, we observe that the
running time significantly increases when the number of
groups increases for EWDCMT. In contrast, the increase
of the running time is not so significant with the number
of groups for EWTM-J, Random, EWTM-L, and Retrieval.
The reason is that EWDCMT has to rebuild whole multicast
trees for minimizing data redundancy, while the other four
algorithms only reconstruct part of the multicast trees to

EMERGING TOPICS
FIGURE 13. Impacts of the number of groups with 500 joining
nodes on the average running time required for each algorithm
under (a) power-law group size distribution and
(b) uniform group size distribution.
FIGURE 14. Impacts of the number of groups with 500 leaving
nodes on the average running time required for each algorithm
under (a) power-law group size distribution and (b) uniform
group size distribution.
satisfy the requests. We also find that the running time
under uniform group size distribution is higher than that
under power-law group size distribution. This is because by
following power-law distribution, most of the groups tend to
be small and then each algorithm spends less time to handle
tree maintenance due to node joining and leaving. The simu-
lation results show that the average running time required by
our proposed algorithms (i.e., EWTM-J and EWTM-L) are
shorter than 600µs for processing a multicast request (flow).
Recent researches indicate that in data centers, 70% of the
flows are delay-sensitive short flows [26], which require their
flow setup time shorter than 1ms [27]. The result confirms
that the our proposed tree maintenance algorithms are
applicable to data centers.
By comparing the algorithm for node joining
(i.e., EWTM-J) and leaving (i.e., EWTM-L), we can observe
an interesting phenomenon. EWTM-J can reduce more data
redundancy when the scale of the system is large. In contrast,
the efficacy of EWTM-J is more evident when the number of
nodes is fewer (e.g., when the group size is 50 with power-
law distribution). Moreover, the performance of EWTM-J
and EWTM-L degrades as the number of the joining/leaving
nodes increases. A open issue is when we should adopt
EWDCMT to rebuild the whole multicast trees of all groups to
gain a better output. In fact, there exists a trade-off between
the system performance and the computational complexity.
System operators can design their policies according to their
system performance requirements. We do not focus on the
issue in this paper, and it can be one of the future directions
for extending the research.
VII. CONCLUSION
In this paper, we have addressed the group communication
issue raised in wireless data center networks. We explored
the multicast tree construction and maintenance problems
with the coexistence of wired and wireless links. The objec-
tive of this paper is to minimize the total multicast traffic.
We proved NP-hardness of the target problems. For the tree
construction problem, we proposed a heuristic algorithm to
efficiently use wireless transmission links. For the tree main-
tenance problem, a low-complexity solution was developed
to adjust the multicast trees when their receivers join/leave.
Finally, we conducted a series of simulations to evaluate
the performance of our proposed algorithms. The simulation
results demonstrated that our proposed algorithms are effec-
tive for reducing the total multicast traffic. We also observed
some useful insights which can be used to the design of
multicast tree construction and maintenance for wireless data
center networks.
REFERENCES
[1] S. Ghemawat, H. Gobioff, and S.-T. Leungm, ‘‘The Google file system,’’
in Proc. 19th ACM SOSP, 2003, pp. 29–43.
[2] J. Dean and S. Ghemawat, ‘‘MapReduce: Simplified data processing on
large clusters,’’ in Proc. 6th Conf. Symp. OSDI, 2004, p. 10.
[3] K. Nagaraj, H. Khandelwal, C. Killian, and R. R. Kompella,
‘‘Hierarchy-aware distributed overlays in data centers using DC2,’’
in Proc. 4th Int. Conf. COMSNETS, Jan. 2012, pp. 1–10.
[4] J. Cao et al., ‘‘Datacast: A scalable and efficient reliable group data delivery
service for data centers,’’ in Proc. ACM 8th Int. Conf. CoNEXT, 2012,
pp. 37–48.
[5] S. Kandula, J. Padhye, and P. Bahl, ‘‘Flyways to de-congest data center
networks,’’ in Proc. ACM Workshop Hot Topics Netw., 2009, pp. 1–6.
[6] D. Halperin, S. Kandula, J. Padhye, P. Bahl, and D. Wetherall,
‘‘Augmenting data center networks with multi-gigabit wireless links,’’ in
Proc. ACM SIGCOMM Conf., 2011, pp. 38–49.
[7] X. Zhou et al., ‘‘Mirror mirror on the ceiling: Flexible wireless links for
data centers,’’ in Proc. ACM SIGCOMM Conf. Appl., Technol., Archit.,
Protocols Comput. Commun., 2012, pp. 443–454.
[8] Y. Katayama, K. Takano, Y. Kohda, N. Ohba, and D. Nakano, ‘‘Wireless
data center networking with steered-beam mmWave links,’’ in Proc. IEEE
WCNC, Mar. 2011, pp. 2179–2184.
[9] J.-Y. Shin, E. G. Sirer, H. Weatherspoon, and D. Kirovski,
‘‘On the feasibility of completely wireless datacenters,’’ IEEE/ACM
Trans. Netw., vol. 21, no. 5, pp. 1666–1679, Oct. 2013.
[10] S. Deering, Host Extensions for IP Multicasting, document RFC 1112,
1989.
[11] B. Cain, S. Deering, I. Kouvelas, B. Fenner, and A. Thyagarajan, Internet
Group Management Protocol, document RFC 3376, 2002.
[12] Y. Yang, J. Wang, and M. Yang, ‘‘A service-centric multicast architecture
and routing protocol,’’ IEEE Trans. Parallel Distrib. Syst., vol. 19, no. 1,
pp. 35–51, Jan. 2008.
[13] D. Li, J. Yu, J. Yu, and J. Wu, ‘‘Exploring efficient and scalable multicast
routing in future data center networks,’’ in Proc. IEEE INFOCOM,
Apr. 2011, pp. 1368–1376.
[14] L. Junhai, Y. Danxia, X. Liu, and F. Mingyu, ‘‘A survey of multicast routing
protocols for mobile ad-hoc networks,’’ IEEE Commun. Surveys Tuts.,
vol. 11, no. 1, pp. 78–91, First Quarter 2009.
[15] J. J. Garcia-Luna-Aceves and E. L. Madruga, ‘‘The core-assisted mesh
protocol,’’ IEEE J. Sel. Areas Commun., vol. 17, no. 8, pp. 1380–1394,
Aug. 1999.
[16] K. Chen and K. Nahrstedt, ‘‘Effective location-guided tree construction
algorithms for small group multicast in MANET,’’ in Proc. 21st Annu. Joint
Conf. IEEE INFOCOM, Jun. 2002, pp. 1180–1189.
[17] J. Biswas, M. Barai, and S. K. Nandy, ‘‘Efficient hybrid multicast routing
protocol for ad-hoc wireless networks,’’ in Proc. 29th Annu. IEEE Int.
Conf. LCN, Nov. 2004, pp. 180–187.

EMERGING TOPICS
IN COMPUTING
[18] Y. Vigfusson et al., ‘‘Dr. multicast: Rx for data center communication
scalability,’’ in Proc. ACM 5th EuroSys, 2010, pp. 349–362.
[19] D. Li, Y. Li, J. Wu, S. Su, and J. Yu, ‘‘ESM: Efficient and scalable
data center multicast routing,’’ IEEE/ACM Trans. Netw., vol. 20, no. 3,
pp. 944–955, Jun. 2012.
[20] M. Al-Fares, A. Loukissas, and A. Vahdat, ‘‘A scalable, commodity
data center network architecture,’’ in Proc. ACM SIGCOMM Conf. Data
Commun., 2008, pp. 63–74.
[21] C. Guo et al., ‘‘BCube: A high performance, server-centric network
architecture for modular data centers,’’ in Proc. ACM SIGCOMM Conf.
Data Commun., 2009, pp. 63–74.
[22] P. Gupta and P. R. Kumar, ‘‘The capacity of wireless networks,’’ IEEE
Trans. Inf. Theory, vol. 46, no. 2, pp. 388–404, Mar. 2000.
[23] M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to
the Theory of NP-Completeness, 1st ed. New York, NY, USA: Freeman,
Jan. 1979.
[24] T. Benson, A. Anand, A. Akella, and M. Zhang, ‘‘Understanding data
center traffic characteristics,’’ in Proc. 1st ACM SIGCOMM Workshop Res.
Enterprise Netw., 2010, pp. 65–72.
[25] S. Kandula, S. Sengupta, A. Greenberg, P. Patel, and R. Chaiken,
‘‘The nature of data center traffic: Measurements & analysis,’’ in Proc. 9th
ACM SIGCOMM Conf. Internet Meas., 2009, pp. 202–208.
[26] T. Benson, A. Akella, and D. A. Maltz, ‘‘Network traffic characteristics of
data centers in the wild,’’ in Proc. 10th ACM SIGCOMM Conf. Internet
Meas., 2010, pp. 267–280.
[27] A. R. Curtis, J. C. Mogul, J. Tourrilhes, P. Yalagandula, P. Sharma, and
S. Banerjee, ‘‘DevoFlow: Scaling flow management for high-performance
networks,’’ in Proc. ACM SIGCOMM Conf., 2011, pp. 254–265.
CHING-CHIH CHUANG (S’13) received the
B.S. degree in computer science and informa-
tion engineering from I-Shou University, in 2008,
and the M.S. degree in computer science
and information engineering from National
Chung Cheng University, in 2010. He is currently
pursuing the Ph.D. degree with the Department of
Computer Science and Information Engineering,
National Taiwan University. His research interests
include data center networks and software defined
networking.
YA-JU YU received the B.S. degree in com-
puter and communication engineering from
the National Kaohsiung First University of
Science and Technology, in 2005, the M.S. degree
in communication engineering from National
Central University, in 2007, and the Ph.D. degree
from the Graduate Institute of Networking and
Multimedia, National Taiwan University, in 2012.
He is currently a Senior Engineer with the Smart
Network System Institute, Institute for Infor-
mation Industry, Taiwan. His research interests include wireless mobile
networks, multimedia communications, and cloud datacenter networking.
AI-CHUN PANG (SM’95) received the B.S.,
M.S., and Ph.D. degrees in computer science
and information engineering from National Chiao
Tung University, Taiwan, in 1996, 1998, and
2002, respectively. She joined the Department
of Computer Science and Information Engineer-
ing, National Taiwan University (NTU), Taipei,
Taiwan, in 2002. She is currently the Director of
the Graduate Institute of Networking and Mul-
timedia (INM), NTU, and a Professor with the
Department of Computer Science and Information Engineering and INM.
She is also an Adjunct Research Fellow with the Research Center for
Information Technology Innovation, Academia Sinica, Taiwan. She has
co-authored a book entitled Wireless and Mobile All-IP Networks
(John Wiley Sons Inc.). Her research interests include the design and
analysis of wireless and multimedia networking, mobile communications,
and cloud data center networking. She was a recipient of the Outstanding
Teaching Award at NTU in 2010, the Investigative Research Award of the
Pan Wen Yuan Foundation in 2006, the Wu Ta You Memorial Award of
the National Science Council in 2007, the Excellent Young Engineer Award
of the Chinese Institute of Electrical Engineering in 2007, and the K. T. Li
Award for Young Researchers of the ACM Taipei/Taiwan Chapter in 2007.
She was also a recipient of the Republic of China Distinguished Women
Medal in 2009. She was a Guest Editor of the IEEE Wireless Communi-
cations, and is an Associate Editor of Wireless Networks and Security and
Communication Networks. She served on the Technical Program Committee
of many international conferences, including the IEEE INFOCOM, the IEEE
GLOBE-COM, the IEEE ICC, and the IEEE VTC.
HSUEH-WEN TSENG (M’11) received the
Ph.D. degrees in computer science and
information engineering from National Taiwan
University, in 2009. He is currently an Assistant
Professor of Computer Science and Engineer-
ing with National Chung Hsing University.
His research interests include cloud computing and
networking, networks-on-chip, design, analysis,
and implementation of network protocols, and
wireless networks.
HSIN-PENG LIN received the B.S. degree
in transportation management from Tamkang
University, in 1996, and the M.S. degree in
transportation and communication management
from National Cheng Kung University, in 1998.
He is currently a Researcher with Chunghwa Tele-
com Laboratories and a part-time Ph.D. Student
with the Graduate Institute of Computer Science
and Information Engineering, National Taiwan
University. His research interests include
multimedia communications, cloud data center networking, and wearable
devices.

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