11f6643-t1b - Fall 2011 CS 6643 Parallel Processing...

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Fall 2011 Practice Questions Answer all questions. Be concise, specific, and give quantitative justifications where needed. Note: p is number of processors; m is message size; t s is startup overhead; t w is per word transfer time; t h is per hop overhead. CT: cut-through; SAF: store-and-forward. 1. (5+5 = 10 points) A. What is its diameter and bisection width (in links) of a 25-processor parallel computer with a 5x5 two- dimensional mesh as its interconnection network? B. If t s = 100 ns, t w =32 ns and t h is ignored, give the time required to send a 100-word message from the leftmost node to the rightmost node in the first row of this network using SAF and CT routing models? 2. (2+2+1 = 5 points) A. Two arrays of n integers are to be added element-wise to obtain a new n -integer array. Give a suitable decomposition method to partition the problem. B. Give the corresponding task-channel graph. C. If p processors are available, how do you agglomerate the primitive tasks into larger tasks with reduced overhead. 3. (3 points) What is the row block-decomposition method? Explain it using a 2-dimensional matrix. 4. (4 points) What is overlapping communication with computation? Explain briefly. 5. (10 points) Suppose, the parallel processing overhead of a parallel system is T o = Θ (np (log p)) . If the sequential time complexity of the problem solved is T 1 = Θ (n 2 ) , give the isoefficiency function of the system. What is the increase in problem size if the number of processors is increased by a factor of 2? 6. (4+6+10=20 points) A. What is the SPMD model? How is it related to SIMD and MIMD parallel architectures? B. Given below is a modified 8x8 Omega network. Show how routes are set up to realize 2 b 5 and 4 b 3 communications. Describe a routing rule based on the destination ID. C. A 16-processor hypercube has links with width of 1 and clock rate of 1 GHz. What is its diameter and bisection bandwidth? If a word is 32 bits, what is t w , the time taken to transfer a word between adjacent processors? If t s
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11f6643-t1b - Fall 2011 CS 6643 Parallel Processing...

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