# Hw4 - Consider using Clique Problem for your reduction http/en.wikipedia.org/wiki/Graph isomorphism problem http/en.wikipedia.org/wiki/Subgraph

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COT 5405 Summer 2009 HW4 1. The assignment problem is usually stated this way: There are n people to be assigned to n jobs. The cost of assigning the i th person to the j th jobs cost( i , j ). You are to develop a branch and bound algorithm that assigns every job to a person and at the same time minimizes the total cost of the assignment. 2. This problem is called the postage stamp problem. Envision a country that issues n diFerent denominations of stamps but allows no more than m stamps on a single letter. ±or given values of m and n , write values, from one on up, and all possible sets of denominations that realize that range. ±or example , for n =4 and m =5, the stamps with values (1, 4, 12, 21) allow the postage values 1 through 71. Are there any other sets of four denominations that have the same range. Use a backtracking algorithm. 3. Given two graphs G 1 and G 2 and check if G 1 is a subgraph of G 2 (Subgraph Isomorphism Problem). Show that this problem is NP-complete.(Hint:
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Unformatted text preview: Consider using Clique Problem for your reduction). http://en.wikipedia.org/wiki/Graph isomorphism problem http://en.wikipedia.org/wiki/Subgraph isomorphism problem 4. An instance of the dominating set problem consists of: a graph G with a set V of vertices and a set E of edges, and a positive integer K smaller than or equal to the number of vertices in G. The problem is to determine whether there is a dominating set of size K or less for G. In other words, we want to know if there is a subset D of V of size less than or equal to K such that every vertex not in D is joined to at least one member of D by an edge in E. Prove that Dominating set problem is NP-complete. (Hint: Consider using Vertex Cover for your reduction) 5. Show that 4-SAT problem is NP-complete. Generalize this to m-SAT, any m ≥ 4. 1...
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## This note was uploaded on 01/15/2012 for the course COT 5405 taught by Professor Ungor during the Fall '08 term at University of Florida.

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