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

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  • Ramaswamy, Ramkumar
  • Orlin, James
  • Chakravarty, Nilopal

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.

Suggested Citation

  • Ramaswamy, Ramkumar & Orlin, James & Chakravarty, Nilopal, 2004. "Sensitivity Analysis for Shortest Path Problems and Maximum Capacity Path Problems in Undirected Graphs," Working papers 4465-03, Massachusetts Institute of Technology (MIT), Sloan School of Management.
  • Handle: RePEc:mit:sloanp:7389
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    File URL: http://hdl.handle.net/1721.1/7389
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    Keywords

    sensitivity analysis; shortest path problem; bottleneck shortest path; maximum capacity path problem;

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