09 - Spring 2010 CS530 Analysis of Algorithms Homework 9 H...

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Unformatted text preview: Spring 2010 CS530 Analysis of Algorithms Homework 9 H OMEWORK 9, DUE A PRIL 21 You must prove your answer to every question. Problems with a ( * ) in place of a score may be a little too advanced, or too challenging to most students, so I do not assign a score to them. But I will still note if you solve them. Problem 1. (15pts) Consider the following problem P 2 : given a graph G decide whether it has a path of length n- 1, where n is the size of the graph. Show that if there is a polynomial algorithm A to solve P 2 then there is a polynomial algorithm to solve the Hamiltonian circuit problem. [ Hint: Use algorithm A repeatedly, after deleting various edges of G . For example, to find out whether there is a path of length n- 1 ending in a given edge at a given point. ] Solution. Take points u , v , connected by an edge e , and another edge f adja- cent to u and yet another edge g adjacent to v (they should not be between u and v ). Deleting all edges from G that are adjacent to u or...
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09 - Spring 2010 CS530 Analysis of Algorithms Homework 9 H...

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