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.
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Bast, Mehlhorn, Schäfer et al. A Heuristic for Dijkstra's Algorithm with Many Targets and Its Use in Weighted Matching Algorithms. Algorithmica 36, 75–88 (2003). https://doi.org/10.1007/s00453-002-1008-z
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DOI: https://doi.org/10.1007/s00453-002-1008-z