A Heuristic for Dijkstra’s Algorithm with Many Targets and Its Use in Weighted Matching Algorithms

Abstract

We consider the single-source many-targets shortest-path (SSMTSP) problem in directed graphs with non-negative edge weights. A source node s and a target set T is specified and the goal is to compute a shortest path from s to a node in T. Our interest in the shortest path problem with many targets stems from its use in weighted bipartite matching algorithms. A weighted bipartite matching in a graph with n nodes on each side reduces to n SSMTSP problems, where the number of targets varies between n and 1.

The SSMTSP problem can be solved by Dijkstra’s algorithm. We describe a heuristic that leads to a significant improvement in running time for the weighted matching problem; in our experiments a speed-up by up to a factor of 10 was achieved. We also present a partial analysis that gives some theoretical support for our experimental findings.

Partially supported by the IST Programme of the EU under contract number IST-1999-14186 (ALCOM-FT).

Funded by the Deutsche Forschungsgemeinschaft (DFG), Graduiertenkolleg (Graduate Studies Program) ‘Quality Guarantees for Computer Systems’, Department of Computer Science, University of the Saarland, Germany.