ALCOMFT-TR-01-18

Kurt Mehlhorn and Guido Sch\"afer
A Heuristic for Dijkstra's Algorithm with Many Targets and its Use in Weighted Matching Algorithms
MPI. Work packages 4 and 5. February 2001.

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.

Postscript file: ALCOMFT-TR-01-18.ps.gz (116 kb).