# A New Dual Algorithm for Shortest Path Reoptimization

## Abstract

Shortest path problems are among the most studied network flow problems, with interesting applications in various fields. In large scale transportation systems, a sequence of shortest path problems must often be solved, where the (*k* + 1)^{ st } problem differs only slightly from the *k* ^{ th } one. Significant reduction in computational time may be obtained from an efficient reoptimization procedure that exploits the useful information available after each shortest path computation in the sequence. Such reduction in computational time is essential in many on-line applications. This work is devoted to the development of such reoptimization algorithm. We shall focus on the sequence of shortest path problems to be solved for which problems differ by the origin node of the path set. After reviewing the classical algorithms described in the literature so far, which essentially show a Dijkstra-like behavior, a new dual approach will be proposed, which could be particularly promising in practice.

## Keywords

Short Path Short Path Problem Close Node Short Path Tree Dual Algorithm## Preview

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