Sensitivity Analysis for Shortest Path Problems and Maximum Capacity Path Problems in Undirected Graphs

Ramkumar Ramaswamy, James B. Orlin and Nilopal Chakravarty

No 4465-03, Working papers from Massachusetts Institute of Technology (MIT), Sloan School of Management

Abstract: This paper addresses sensitivity analysis questions concerning the shortest path problem and the maximum capacity path problem in an undirected network. For both problems, we determine the maximum and minimum weights that each edge can have so that a given path remains optimal. For both problems, we show how to determine these maximum and minimum values for all edges in O(m + K log K) time, where m is the number of edges in the network, and K is the number of edges on the given optimal path.

Keywords: sensitivity analysis; shortest path problem; bottleneck shortest path; maximum capacity path problem (search for similar items in EconPapers)
Date: 2004-04-30
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