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# 4hw - (a Determine whether a system with the test graph...

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ECE/CS 598NV Special Topics (Distributed Algorithms) Fall 2010 Homework 4 Total points: 20 Due: 9:30 a.m. on November 2, 2010 1. (5 points) Problem 8.1 in the textbook.

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2. (5 points) This question relates to the paper on weighted voting by Tong and Kain. Consider a system consisting of four nodes, named 1, 2, 3, and 4, with the probability p i that node i is operational as follows: p 1 = p 2 = 4 5 p 3 = p 4 = 8 9 (a) Suggest a vote assignment that maximizes the reliability. (b) Determine the active subsets achieved with your vote assignment. (Or, alternatively, determine the quorum system obtained with your vote assignment.)
3. (5 points) This question relates to system-level diagnosis, with the symmetric invalidation model for permanent faults (see section 3.1 of the paper by Somani).

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Unformatted text preview: (a) Determine whether a system with the test graph below is t-diagnosable for (i) t = 1 and (ii) t = 2. B C E F G H A D Explain your answers. (i) t = 1 (ii) t = 2 (b) State true or false with explanation : A test graph of n nodes with n > 2 t and connectivity t is t-diagnosable. 4. (5 points) This question relates to the tech report on equality computation by Liang and Vaidya. Present an algorithm for the MEQ-AD(3,5) problem. Your algorithm should have the property that the values sent by each node depend entirely on its initial input. Represent your answer using a bipartite graph as in the example in Figure 2 of the report. Recommended exercise: Determine whether your algorithm is optimal....
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