# hw3 - Homework 3 CSE 450/598 Spring 2010 Arizona State...

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Unformatted text preview: Homework 3 CSE 450/598 Spring 2010 Arizona State University Due: Thursday 2/11 before 10:30 1. (4.2) For each of the following statements, decide whether it is true or false. If it is true, give a short explanation. If it is false, give a counterexample. (a) Suppose we are given an instance of the Minimum Spanning Tree problem on a graph G , with edge costs that are all positive and distinct. Let T be a minimum spanning tree for this instance. Now suppose we replace each edge cost c e by its square c 2 e , thereby creating a new instance of the problem with the same graph but different costs. True or false? T must still be a minimum spanning tree for this new instance. (b) Suppose we are given an instance of the Shortest s- t Path problem on a directed graph G . We assume that all edge costs are positive and distinct. Let P be a minimum-cost s- t path for this instance. Now suppose we replace each edge cost c e by its square c 2 e , thereby creating a new instance of the problem with the same graph but different costs. True or false? P must still be a minimum-cost s- t path for this new instance. 2. (4.13) A small business—say, a photocopying service with a single large machine— faces the following scheduling problem. Each morning they get a set of jobs from customers. They want to do the jobs on their single machine in an order that keeps their customers happiest....
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hw3 - Homework 3 CSE 450/598 Spring 2010 Arizona State...

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