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# hw3 - IE 418 Integer Programming Problem Set#3 Due Date...

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IE 418 – Integer Programming Problem Set #3 Due Date: April 4 Do the following problems. You may work with one other classmate. If you work alone, you will receive a 10% bonus. You are allowed to examine outside sources, but you must cite any references that you use. Please don’t discuss the problems with other members of the class (other than your partner, if you are working with one). 1 Reductions These Problems are NP -Complete PROBLEM: Number Partition Problem (NPP) INSTANCE: Finite set N of items, each with size s n Z + n N , and an integer K . QUESTION: Does there exist a subset N N such that n N s n = n N \ N s n ? PROBLEM: Vertex Cover Problem (VCP) INSTANCE: Graph G = ( V, E ), and a positive integer K ≤ | V | . QUESTION: Is there a vertex cover of size K or less in G. (Does there exist a subset V V with | V | ≤ K such that for each edge e = ( u, v ) E either u V or v V )? 1.1 Problem Show that the Dominating Set Problem (DSP) is NP -Complete: PROBLEM: Dominating Set Problem (DSP) INSTANCE: Graph G = (

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hw3 - IE 418 Integer Programming Problem Set#3 Due Date...

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