hw5 - AMS/MBA 546 (Fall, 2010) Estie Arkin Network Flows...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: AMS/MBA 546 (Fall, 2010) Estie Arkin Network Flows Homework Set # 5 Due Thursday, October 14, 2010. 1). Show that the following problems are NP-complete. You may use reductions from any of the problems shown NP-complete by Karp (3SAT, 3 dimensional matching, partition, vertex cover, Hamilton cycle/path, or clique), or any other problem discussed in class. Remember to also show the problem is in NP. (a). Given G = ( N,E ), is there a spanning tree T of G such that the nodes of T have degree at most 2? (b). Given G = ( N,E ), is there a spanning tree T of G such that the nodes of T have degree at most 3? 2). Recall that a graph is 2-connected if there does not exist a node whose removal disconnects the graph (an articulation node ). Given a graph with positive edge weights, consider the problem of trying to find a minimum weight spanning subgraph that is 2-connected. (This may remind you of the minimum spanning tree problem, in which we look for a subgraph that is 1-connected.) (a). Does the following algorithm work (for all graphs)? Prove or give a counterexample: Sort the edges(a)....
View Full Document

This note was uploaded on 01/31/2011 for the course AMS 546 taught by Professor Arkin,e during the Fall '08 term at SUNY Stony Brook.

Ask a homework question - tutors are online