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hw5(5) - CS 473G Combinatorial Algorithms Fall 2005...

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CS 473G: Combinatorial Algorithms, Fall 2005 Homework 5 Due Thursday, November 17, 2005, at midnight (because you really don’t want homework due over Thanksgiving break) Name: Net ID: Alias: Name: Net ID: Alias: Name: Net ID: Alias: Name: Net ID: Alias: Homeworks may be done in teams of up to three people. Each team turns in just one solution; every member of a team gets the same grade. Neatly print your name(s), NetID(s), and the alias(es) you used for Homework 0 in the boxes above. Attach this sheet (or the equivalent information) to the top of your solution to problem 1. If you are an I2CS student, print “(I2CS)” next to your name. Teams that include both on-campus and I2CS students can have up to four members. Any team containing both on-campus and I2CS students automatically receives 3 points of extra credit. Problems labeled are likely to require techniques from next week’s lectures on cuts, flows, and matchings. See also Chapter 7 in Kleinberg and Tardos, or Chapter 26 in CLRS. 1. Suppose you are asked to construct the minimum spanning tree of a graph G , but you are not completely sure of the edge weights. Specifically, you have a conjectured weight ˜ w ( e ) for every edge e in the graph, but you also know that up to k of these conjectured weights are wrong. With the exception of one edge e whose true weight you know exactly, you don’t know which edges are wrong, or even how they’re wrong; the true weights of those edges could be larger or smaller than the conjectured weights.
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