A hierarchical Algorithm to Solve the Shortest Path Problem in Valued Graphs
<|reference_start|>A hierarchical Algorithm to Solve the Shortest Path Problem in Valued Graphs: 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.<|reference_end|>
@article{koskas2003a,
    title={A hierarchical Algorithm to Solve the Shortest Path Problem in Valued
  Graphs},
    author={Michel Koskas},
    journal={arXiv preprint arXiv:cs/0310019},
    year={2003},
    archivePrefix={arXiv},
    eprint={cs/0310019},
    primaryClass={cs.DS cs.DM}
}