# hw9 - Introduction to Algorithms CS 482 Spring 2006 Problem...

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Introduction to Algorithms Problem Set 9 CS 482 Spring 2006 Due: Friday, April 21 Please hand in each problem on separate sheets with your name and netID on each. If a problem requires multiple sheets, please staple the sheets for that problem together Reading: Chapters 10.1, 10.2, 11.1 - 11.4, 11.8. Question 1 Show that for any fixed constant k 2, determining whether or not an undirected graph G has a spanning tree T with exactly k leaves is NP-Complete. Question 2 Suppose we have an undirected graph G = ( V, E ) with edges costs c e 0 for each edge e E , and a set of nodes S V . Done. Recall that a Steiner tree for S is a tree T in G that spans all nodes in S . As you’ve seen in class, in general, finding the minimum cost Steiner tree is NP-Complete. (a) Give a polynomial time algorithm to find the minimum cost Steiner tree in the case that | S | = 3. (b) Give a 2-approximation for the problem of finding a minimum cost Steiner tree (for any set S ).

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