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CS646: Assignment

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1) Odd-Even Merging Network :

a) State and prove the strategy used in Odd-Even Merging Network. b) Explain how it can be used to sort n elements. c) Determine the number of parallel steps and comparators needed in

the network to sort n elements.

Solution: Please refer Lecture No: 7.

2) Mesh Connected Computer :

a) Write an algorithm to multiply two matrices, each of size n x n on 2-D Mesh Connected Computer having n

2 processors.

b) Determine its time complexity. c) Discuss how this algorithm can be used to determine whether there

exists a path between any two vertices in a graph.

Solution: Please refer Lecture No: 18.

3) Lexicographic Combination:

If the first m elements of the th lexicographic combination X() are a1, a2, ...., am then show that satisfies the following:

n- am

Cr-m+1 nCr - 1 km-1

n- akCr-k+1 -

n- am +1Cr-m+1

Given a combination, explain a method which can be used to generate

the next lexicographic combination.

Solution: Please refer Lecture No: 21.

4) kth Element (EREW model) : Is it possible to design a cost optimal parallel algorithm to find the k

th

element on EREW model? Justify.

Solution: Please refer Lecture No: 14.

5) kth Smallest Element in X+Y (CREW algorithm):

Let X and Y be two sorted sequences of n elements each. Then,

a) Define UBL which is a portion of X+Y and can contain the k

th smallest

element in X+Y.

b) Write a CREW algorithm to find the kth

smallest element in X+Y =

{xi + yj | xi belong to X, yj belong to Y, for all i,j}.

Solution: Please refer Lecture No: 16.

6) Bitonic merge : a) State and prove the theorem of Bitonic merge. b) Write the Biotonic sort algorithm to sort 2

n elements using a

Hypercube with 2n processors.

c) Derive its time complexity.

Solution: Please refer Lecture No: 8 and 11.

7) Merging Algorithm (EREW model) : a) Write a cost optimal merging algorithm for EREW model. b) Derive its time complexity. c) Determine the condition for which the algorithm becomes the cost

optimal.

Solution: Please refer Lecture No: 13.

The Books Referred:

[A]

The Design and Analysis of Parallel Algorithms by Selim G. Akl (Apr 1989)

[B]

Parallel Sorting Algorithms (Notes and Reports in Computer Science and Applied Mathematics, 12)

by Selim G. Akl (Oct 1985)

[C]

Parallel Computation: Models and Methods by Selim G. Akl (Nov 6, 1996)

[D]

Foundations of parallel processing, Ratan K Ghosh, Rajat Moona, Phalguni Gupta, Narosa

Publishing House, 1995