CS6363: Computer Algorithms
Spring 2008
Assignment 8

Due: Wednesday, April 23 (in class)


1. Ex. 23.1-3 (page 566).  Do not assume that the minimum spanning tree
   is computed by Prim, Kruskal or the generic MST algorithm.  All you
   are given is that T is an MST and (u,v) is an edge in T.  From this
   you have to show that there is a cut for which (u,v) is a light edge.

2. Ex. 23.1-11 (page 567).  Modify MST when edge weight is decreased.

3. Problem 23-3, parts a and b (page 577).  Bottleneck spanning tree.

4. Ex. 26.2-2 (page 663).  Execution of Edmonds-Karp flow algorithm.
   After finding a maximum flow, find a minimum cut in the network 
   using the method used in the proof of the max-flow min-cut theorem.

Extra credit: Problem 23-1 (page 575).  Second-best MST.
Extra credit: Ex. 26.3-4 (page 669).  Hall's theorem.