All-Pairs Shortest Paths Algorithm for High-dimensional Sparse Graphs

TL;DR

This paper introduces a novel 'disassembly and assembly' algorithm for solving the all-pairs shortest paths problem on high-dimensional sparse graphs, leveraging solutions from smaller graphs to improve efficiency.

Contribution

It presents a new algorithm that efficiently computes shortest paths in high-dimensional sparse graphs by decomposing and reconstructing the graph structure.

Findings

The proposed algorithm outperforms classic algorithms on benchmark data.

It effectively handles high-dimensional sparse graphs.

The method demonstrates improved computational efficiency.

Abstract

Here the All-pairs shortest path problem on weighted undirected sparse graphs is being considered. For the problem considered, we propose ``disassembly and assembly of a graph'' algorithm which uses a solution of the problem on a small-dimensional graph to obtain the solution for the given graph. The proposed algorithm has been compared to one of the fastest classic algorithms on data from an open public source.