Algorithmica

, Volume 36, Issue 1, pp 75–88 | Cite as

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

  • Bast
  • Mehlhorn
  • Schäfer
  • Tamaki
Article

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 12 was achieved. We also present a partial analysis that gives some theoretical support for our experimental findings.

Keywords

Single-source shortest-path problem, Dijkstra's algorithm, Weighted bipartite matching problem, Assignment problem 

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Copyright information

© Springer-Verlag New York Inc. 2002

Authors and Affiliations

  • Bast
    • 1
  • Mehlhorn
    • 1
  • Schäfer
    • 1
  • Tamaki
    • 1
  1. 1.Max-Planck-Institut für Informatik, Stuhlsatzenhausweg 85, 66123 Saarbrücken, bast@mpi-sb.mpg.de, mehlhorn@mpi-sb.mpg.de, schaefer@mpi-sb.mpg.de, tamaki@mpi-sb.mpg.de.Germany

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