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Unformatted text preview: CS231: Topics in Combinatorial Algorithms Prof. Suri Homework Assignment 3 Handed Out: Nov. 2 Due: Nov. 9 1. Given a flow network G , there can be multiple s – t mincuts (cuts of minimum capacity). Among all these cuts, we want to find one with the fewest number of edges. Propose an efficient (polynomial-time) algorithm to find such a mincut. Be sure to argue its correctness and analyze its time complexity. 2. You have been called in to help diagnose a network failure problem. The network is modeled as a directed graph G = ( V,E ), in which each edge has capacity 1, and there is a source node s and a sink node t . Assume that each node in G lies on at least one path from s to t . When the network is operating smoothly, the maximum s – t flow in G has value k . However, due to an attack by a hacker who has destroyed some of the edges in the network, there is no path from s to t in the remaining (surviving) set of edges. The network administrator believes that the hacker has destroyed precisely...
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- Fall '09