Sensitivity analysis for shortest path problems and maximum capacity path problems in undirected graphs

Authors:
Ramkumar Ramaswamy;James B. Orlin;Nilopal Chakravarti
Affiliations:
Infosys Technologies Limited, 3rd Cross, 561 229, Electronics City, Bangalore, India;MIT E40-147, 3rd Cross, 02139, Cambridge, MA, USA;Ortec Asia, 30 Cecil Street, 02139, Cambridge, MA, Singapore
Venue:
Mathematical Programming: Series A and B
Year:
2005

Citing 0
Cited 5

Bottleneck flows in unit capacity networks

Information Processing Letters
Lower tolerance-based Branch and Bound algorithms for the ATSP

Computers and Operations Research
Some basics on tolerances

AAIM'06 Proceedings of the Second international conference on Algorithmic Aspects in Information and Management
Approximating the stability region for binary mixed-integer programs

Operations Research Letters
Stability measure for a generalized assembly line balancing problem

Discrete Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

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.