# ps7 - Massachusetts Institute of Technology Handout 20...

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Unformatted text preview: Massachusetts Institute of Technology Handout 20 6.046J/18.410J: Introduction to Algorithms April 25, 2003 Professors Piotr Indyk and Bruce Tidor Problem Set 7 This problem set is due at the beginning of class on Thursday, May 8, 2003 . Each problem is to be done on a separate sheet (or sheets) of paper. Mark the top of each sheet with your name, 6.046J/18.410J, the problem number, your recitation section, the date, and the names of any students with whom you collaborated. Problem 7-1. Integral Flows An important issue with network flow problems is that of integrality. A flow through a graph G is said to be integral if the flow on every edge of G is an integer. If the flow on any edge is not an integer, we say the flow is fractional . If the capacity of every edge in G is an integer, then it is not difficult to see that the Ford- Fulkerson algorithm and its variants (e.g. Edmonds-Karp) will always compute an integral flow. This is easy to prove by induction on the number of iterations performed by the algorithm, by noting that we always augment flow in integer amounts, thereby maintaining...
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ps7 - Massachusetts Institute of Technology Handout 20...

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