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The greedy algorithm for set cover is the following: |
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The greedy algorithm for weighted set cover is the following: |
Exercises1. The partial set cover problem is, given a collection of sets and an integer K, to find a minimum number of sets covering all but some K of the elements. Prove that this problem has a (1+ln(n))-approximation algorithm, where n is the number of elements. 2. Given a set of vertices V and a collection of sets of edges E1, E2, …, Em, find a minimum-size collection of the edge sets so that the union of the chosen sets contains a spanning tree. Given a (1+ln(n))-approximation algorithm, where n is the number of vertices. 3. Extend your analyses above to the weighted versions of the problems. |