This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Fall 2011 CMSC 451: Homework 6 Clyde Kruskal Due at the start of class Thursday, December 8, 2011. We know a number of problems are NPcomplete including: Circuit SAT, SAT, 3SAT, Independent Set, Vertex Cover, Hamiltonian Cycle, Traveling Salesman, 3Dimensional Matching, Graph Coloring, Subset Sum, Clique, and Subgraph Isomorphism. Problem 1. HAMILTONIAN PATH PROBLEM: given a directed graph, does it contain a simple path that goes through every vertex exactly once? HAMILTONIAN CYCLE PROBLEM: given a directed graph, does it contain a di rected simple cycle that goes through each vertex exactly once? Assume that the HAMILTONIAN PATH PROBLEM is known to be NPcomplete. Given this assumption, prove that the HAMILTONIAN CYCLE PROBLEM is NP complete. (Make sure to show that the HAMILTONIAN CYCLE PROBLEM is in NP .) Problem 2. Consider the problem DENSE SUBGRAPH: Given G , does it contain a sub graph H that has exactly K vertices and at least Y edges? Prove that this problem is NPcomplete.complete....
View
Full
Document
This note was uploaded on 01/13/2012 for the course CMSC 451 taught by Professor Staff during the Fall '08 term at Maryland.
 Fall '08
 staff

Click to edit the document details