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

TL;DR

This paper introduces a hierarchical algorithm using radix trees for solving the shortest path problem in valued graphs, achieving better performance than traditional algorithms like Dijkstra's.

Contribution

It presents a novel hierarchical algorithm with radix trees that improves the computational complexity for shortest path problems in valued graphs.

Findings

Significantly faster performance compared to existing algorithms

Complexity of $O(D \log v)$ versus Dijkstra's $O(e \\log v)$

Effective in large, valued graphs with hierarchical structure

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.