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A hierarchical Algorithm to Solve the Shortest Path Problem in Valued Graphs

Michel Koskas
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Abstract

This paper details a new algorithm to solve the shortest path problem in valued graphs. Its complexity is $O(D \log v)$ where $D$ is the graph diameter and $v$ its number of vertices. This complexity has to be compared to the one of the Dijkstra's algorithm, which is $O(e\log v)$ where $e$ is the number of edges of the graph. This new algorithm lies on a hierarchical representation of the graph, using radix trees. The performances of this algorithm show a major improvement over the ones of the algorithms known up to now.

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Michel Koskas. 2003-10-10. A hierarchical Algorithm to Solve the Shortest Path Problem in Valued Graphs. https://arxiv.org/abs/cs/0310019

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