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# hbs10(1) - weighted graph G the length of the shortest...

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CS 473 HBS 10 Spring 2009 CS 473: Undergraduate Algorithms, Spring 2009 HBS 10 1. Consider the following problem, called BOX-DEPTH : Given a set of n axis-aligned rectangles in the plane, how big is the largest subset of these rectangles that contain a common point? (a) Describe a polynomial-time reduction from BOX-DEPTH to MAX-CLIQUE . (b) Describe and analyze a polynomial-time algorithm for BOX-DEPTH . [ Hint: O ( n 3 ) time should be easy, but O ( n log n ) time is possible. ] (c) Why don’t these two results imply that P = NP ? 2. Suppose you are given a magic black box that can determine in polynomial time, given an arbitrary
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Unformatted text preview: weighted graph G , the length of the shortest Hamiltonian cycle in G . Describe and analyze a polynomial-time algorithm that computes, given an arbitrary weighted graph G , the shortest Hamiltonian cycle in G , using this magic black box as a subroutine. 3. Prove that the following problems are NP-complete. (a) Given an undirected graph G , does G have a spanning tree in which every node has degree at most 17? (b) Given an undirected graph G , does G have a spanning tree with at most 42 leaves? 1...
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