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A Heuristic for Dijkstra's Algorithm With Many Targets and its Use in Weighted Matching Algorithms

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Mehlhorn,  Kurt
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Schäfer,  Guido
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Citation

Mehlhorn, K., & Schäfer, G. (2001). A Heuristic for Dijkstra's Algorithm With Many Targets and its Use in Weighted Matching Algorithms. In Proceedings of the 9th Annual European Symposium on Algorithms (ESA-01) (pp. 242-253). Berlin, Germany: Springer.


Cite as: https://hdl.handle.net/11858/00-001M-0000-000F-314B-6
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.