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

Authors:
Kurt Mehlhorn;Guido Schäfer
Affiliations:
-;-
Venue:
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Year:
2001

Citing 3
Cited 0

Efficient algorithms for finding maximum matching in graphs

ACM Computing Surveys (CSUR)
LEDA: a platform for combinatorial and geometric computing

LEDA: a platform for combinatorial and geometric computing
Implementation of O (nm log n) Weighted Matchings in General Graphs. The Power of Data Structures

WAE '00 Proceedings of the 4th International Workshop on Algorithm Engineering

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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.