The Multiple Pairs Shortest Path Problem for Sparse Graphs: Exact Algorithms

Abstract

In this paper, we propose two exact algorithms based on the computation of the Dijkstra tree to solve the multiple pairs shortest path problem. Traditionally, to solve this kind of problems, algorithms are based on distance matrices. For sparse graphs, the computation of these matrices is too costly. The two approaches that we propose allow tackling this issue by computing a small number of Dijkstra trees. We test our algorithms on telecommunication network instances and random instances, and we discuss the dependence of the obtained results on the structure of sources and destinations of commodities. We also propose an extension of the Bi-Dijkstra algorithm to consider several destinations together.