Parallel Algorithms

Aug 26, 20202 likes695 views

The document discusses the Random Access Machine (RAM) model of computation. The RAM model allows algorithms to be measured in a machine-independent way based on performance. It assumes a single processor where instructions are executed sequentially with no concurrency. The running time of an algorithm is the number of time steps, and space used is the number of memory cells. The RAM makes assumptions like each operation taking one time step and unlimited memory access.

B Y
DR. HEMAN PATHAK
Associate Professor
Dept. of Comp. Sc., KGC - Dehradun
1
Book
PARALLEL COMPUTING
THEORY AND PRACTICE
By Michel J. Quinn
CHAPTER – 2

2
This paper is about the
designing of efficient
algorithms for real parallel
computers

Random Access Machine (RAM)
Algorithms can be measured in a machine-independent
way using the Random Access Machine (RAM) model. This
model of computation is an abstraction that allows us to
compare algorithms on the basis of performance.
 This model assumes a single processor.
 In the RAM model, instructions are executed one after
the other, with no concurrent operations.
3

4
The assumptions made in the RAM are:
 Each simple operation takes 1 time step.
 Loops and subroutines are not simple operations.
 Each memory access takes one time step, and there is no
shortage of memory.
 For any given problem the running time of an algorithms is
assumed to be the number of time steps. The space used by
an algorithm is assumed to be the number of RAM memory
cells.
Random Access Machine (RAM)

Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm
5

Sequential Algorithm
Sum = 0
for i = 0 to n-1 do
sum = sum + a[i]
endfor
Time Complexity = (n)
20
Sum of n elements

Sequential algorithm
for i = 1 to n-1 do
a[i] = a[i-1] + a[i]
endfor
Time Complexity = (n)
27
Prefix Sum

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The escalating energy crisis, heightened environmental awareness and the impacts of climate change have driven global efforts to reduce carbon emissions. A key strategy in this transition is the adoption of green energy technologies particularly for charging electric vehicles (EVs). According to the U.S. Department of Energy, EVs utilize approximately 60% of their input energy during operation, twice the efficiency of conventional fossil fuel vehicles. However, the environmental benefits of EVs are heavily dependent on the source of electricity used for charging. This study examines the potential of renewable energy (RE) as a sustainable alternative for electric vehicle (EV) charging by analyzing several critical dimensions. It explores the current RE sources used in EV infrastructure, highlighting global adoption trends, their advantages, limitations, and the leading nations in this transition. It also evaluates supporting technologies such as energy storage systems, charging technologies, power electronics, and smart grid integration that facilitate RE adoption. The study reviews RE-enabled smart charging strategies implemented across the industry to meet growing global EV energy demands. Finally, it discusses key challenges and prospects associated with grid integration, infrastructure upgrades, standardization, maintenance, cybersecurity, and the optimization of energy resources. This review aims to serve as a foundational reference for stakeholders and researchers seeking to advance the sustainable development of RE based EV charging systems.

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In the world of technology, Jacob Murphy Australia stands out as a Junior Software Engineer with a passion for innovation. Holding a Bachelor of Science in Computer Science from Columbia University, Jacob's forte lies in software engineering and object-oriented programming. As a Freelance Software Engineer, he excels in optimizing software applications to deliver exceptional user experiences and operational efficiency. Jacob thrives in collaborative environments, actively engaging in design and code reviews to ensure top-notch solutions. With a diverse skill set encompassing Java, C++, Python, and Agile methodologies, Jacob is poised to be a valuable asset to any software development team.

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Several studies have established that strength development in concrete is not only determined by the water/binder ratio, but it is also affected by the presence of other ingredients. With the increase in the number of concrete ingredients from the conventional four materials by addition of various types of admixtures (agricultural wastes, chemical, mineral and biological) to achieve a desired property, modelling its behavior has become more complex and challenging. Presented in this work is the possibility of adopting the Gene Expression Programming (GEP) algorithm to predict the compressive strength of concrete admixed with Ground Granulated Blast Furnace Slag (GGBFS) as Supplementary Cementitious Materials (SCMs). A set of data with satisfactory experimental results were obtained from literatures for the study. Result from the GEP algorithm was compared with that from stepwise regression analysis in order to appreciate the accuracy of GEP algorithm as compared to other data analysis program. With R-Square value and MSE of -0.94 and 5.15 respectively, The GEP algorithm proves to be more accurate in the modelling of concrete compressive strength.

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The main purpose of the current study was to formulate an empirical expression for predicting the axial compression capacity and axial strain of concrete-filled plastic tubular specimens (CFPT) using the artificial neural network (ANN). A total of seventy-two experimental test data of CFPT and unconfined concrete were used for training, testing, and validating the ANN models. The ANN axial strength and strain predictions were compared with the experimental data and predictions from several existing strength models for fiber-reinforced polymer (FRP)-confined concrete. Five statistical indices were used to determine the performance of all models considered in the present study. The statistical evaluation showed that the ANN model was more effective and precise than the other models in predicting the compressive strength, with 2.8% AA error, and strain at peak stress, with 6.58% AA error, of concrete-filled plastic tube tested under axial compression load. Similar lower values were obtained for the NRMSE index.

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Parallel Algorithms

1. B Y DR. HEMAN PATHAK Associate Professor Dept. of Comp. Sc., KGC - Dehradun 1 Book PARALLEL COMPUTING THEORY AND PRACTICE By Michel J. Quinn CHAPTER – 2

2. 2 This paper is about the designing of efficient algorithms for real parallel computers

3. Random Access Machine (RAM) Algorithms can be measured in a machine-independent way using the Random Access Machine (RAM) model. This model of computation is an abstraction that allows us to compare algorithms on the basis of performance.  This model assumes a single processor.  In the RAM model, instructions are executed one after the other, with no concurrent operations. 3

4. 4 The assumptions made in the RAM are:  Each simple operation takes 1 time step.  Loops and subroutines are not simple operations.  Each memory access takes one time step, and there is no shortage of memory.  For any given problem the running time of an algorithms is assumed to be the number of time steps. The space used by an algorithm is assumed to be the number of RAM memory cells. Random Access Machine (RAM)

5. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 5

6. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 6

7. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 7

8. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 8

9. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 9

10. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 10

11. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 11

12. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 12

13. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 13

14. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 14

15. 15

16. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 0 1 1 2 2 4 3 8 : : p 2p lb(x) or log2(x): Log base 2, also known as the binary logarithm, is the logarithm to the base 2. The binary logarithm of x is the power to which the number 2 must be raised to obtain the value x. log2(1) = 0 log2(2) = 1 log2(4) = 2 log2(8) = 3 log2(16) = 4 log2(32) = 5 p steps for 2p Processors log2(p) steps for log2(2p)=p Processors If p is perfect power of 2 otherwise log2(p)

17. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm

18. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 18

19. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 19

20. Sequential Algorithm Sum = 0 for i = 0 to n-1 do sum = sum + a[i] endfor Time Complexity = (n) 20 Sum of n elements

21. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 21

22. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 22

23. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 23 Step 1: PEs Required 𝑛/2 Step 2: PEs Numbers i = 0 to 𝑛/2 -1 Step 3: Sequential Loop j = 0 to log 𝑛 -1 Step 4: Which PEs will participate i mod 2j =0 and 2i+ 2j < n Step 5: What is to be done in each step A[2i] = A[2i] + A[2i + 2j ]

24. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 24

25. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 25

26. 26 Prefix Sum

27. Sequential algorithm for i = 1 to n-1 do a[i] = a[i-1] + a[i] endfor Time Complexity = (n) 27 Prefix Sum

28. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 28

29. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 29

30. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 30

31. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 31

32. 32 List Ranking

33. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 33

34. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 34

35. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 35

36. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 36

37. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 37

38. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 38

39. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 39

40. 40 Pre-order Tree Traversal

41. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 41

42. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 42 EXAMPLE

43. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 43 AB BD DB BE EC CE EH HE EB BA AC CF FC CA 1 1 0 1 1 0 1 0 0 0 1 1 0 0 EXAMPLE No. of Vertices = 8 (n) No. of edges = 7 (n-1) Forward edges = 7 (n-1) Backward edges = 7 (n-1) Total Edges = 14 2(n-1)

44. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 44 EXAMPLE

45. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 45 EXAMPLE (C,F) Vertices A B C D E F G H Positions 1 7 2 6 5 1 4 3 Prorder 1 2 7 3 4 8 5 6

46. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 46

47. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 47

48. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 48

49. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 49

50. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 50

51. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 51

52. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 52

53. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 53

54. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 54

55. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 55

56. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 56

57. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 57

58. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 58

59. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 59

60. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 60

61. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 61

62. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 62

63. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 63

64. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 64

65. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 65

66. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 66

67. Slides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htmSlides & Diagrams from: http://cse.iitkgp.ac.in/~debdeep/courses_iitkgp/PAlgo/index.htm 67

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