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

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This paper details a new algorithm to solve the shortest path problem in valued graphs. Its complexity is O(D 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 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.