hw6 (1) - COMS 4231 Analysis of Algorithms I Fall 2010...

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COMS 4231: Analysis of Algorithms I, Fall 2010 Problem Set 6, due Tuesday December 7, in class Note: We plan to post solutions on Tuesday after the class, in preparation for the final, so no late homeworks will be accepted. Please follow the homework submission guidelines posted on the web As usual, for each of the algorithms that you give, include an explanation of how the algorithm works, why it is correct, what is its running time, and why it has the claimed running time. Problem 1 . a. Exercise 24.3-2 in CLRS, page 663. b. Exercise 24.3-4 in CLRS, page 663. Problem 2. Do Problem 24-1 in CLRS, page 678. Problem 3 . Do Problem 26-3 (“Algorithmic consulting”) in CLRS, page 761. Problem 4 . The Maximum Independent Set (MIS) problem is as follows: Given an undirected graph G=(N,E), find a maximum-size set S of nodes that are pairwise non- adjacent, i.e. there is no edge connecting any two nodes of S (such a set of nodes is called independent). 1. Give an efficient algorithm to solve the MIS problem when G is bipartite.
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