MIT6_042JF10_rec10

MIT6_042JF10_rec10 - 6.042/18.062J Mathematics for Computer...

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6.042/18.062J Mathematics for Computer Science October 13, 2010 Tom Leighton and Marten van Dijk Problems for Recitation 10 Analysis of Two Networks Two communication networks are shown below. Complete the table of properties and be prepared to justify your answers. IN 0 IN 1 IN 2 IN 3 IN 4 OUT 0 OUT 1 OUT 2 OUT 3 OUT 4 IN IN IN IN OUT OUT OUT OUT 0 1 2 2 3 3 0 1 5-Path 4-Cycle network # switches switch size diameter max congestion 5-path 4-cycle Recall that the diameter of a communication network is the number of edges on the shortest path between the input and output that are farthest apart. The max congestion of a network is the largest number of packets that pass through any switch in the best solution to the hardest permutation routing problem. You might imagine that your enemy picks a permutation and then you pick the path taken by each packet. (Her goal is to cause congestion, and yours is to eliminate it.) Assuming you both do your best, the max congestion is then equal to the largest number of packets passing
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