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CSE 441T/541T Advanced Algorithms Fall 2008 Homework 4a: More NP-Completeness, and Approximation Assigned: October 29, 2008 Due Date: November 5, 2008 For NP-completness reductions, unless otherwise indicated, you should reduce from one of: SAT, 3-SAT, SUBSET-SUM, PARTITION, CLIQUE, INDEPENDENT SET, or VERTEX COVER. You must submit your homework with a signed cover sheet attached to the front. Core Problem 1. (15 pts) In class, we showed that INDEPENDENT-SET ≤ p VERTEX-COVER. Recall that a graph G with n vertices has an independent set of size at least k iﬀ it has a vertex cover of size at most n - k ; in particular, the vertices not in the cover form an independent set. In class, we saw a 2-approximation algorithm A for ﬁnding the minimal vertex cover. Pro- fessor Ptolemy suggests that one can derive a constant-factor approximation algorithm for independent set by ﬁrst reducing it to a vertex cover problem as above, then applying algo- rithm A . Is the professor correct? Justify your answer, either by proving that there exists a
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This note was uploaded on 11/13/2009 for the course CSE 441 taught by Professor Cse441 during the Spring '08 term at Washington University in St. Louis.
- Spring '08