CSE331 HW6 - CSE 331 Introduction to Algorithm Analysis and...

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CSE 331: Introduction to Algorithm Analysis and Design Fall 2011 Homework 6 Due Friday, October 28, 2011 by 1:15pm in class IMPORTANT: Please submit each problem separately, i.e. each problem should begin on a new page and only the pages for one problem should be stapled together. Failure to do so might result in some problem(s) not being graded. For general homework policies and our suggestions, please see the policy document. 1. (40 points ) Say we are given an instance of the shortest s - t path problem on a directed graph G . Assume that all the edge weights are distinct and positive. Let P be a minimum cost path for this instance. Now consider a new instance where each edge cost c e is replaced by a new edge cost of c 3 e (but the graph G remains the same). Mr. GraphKnowItAll claims that P is still a minimum cost s - t path in the new instance. Decide if Mr. GraphKnowItAll is full of it or not– if so, give a counter example. If not, give a short explanation why Mr. GraphKnowItAll is correct.
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