Fast One-to-Many Multicriteria Shortest Path Search

TL;DR

This paper presents a new algorithm for fast one-to-many multicriteria shortest path searches that combines preprocessing, dimensionality reduction, and heuristics to significantly improve speed and memory efficiency.

Contribution

It introduces a novel combination of preprocessing and dimensionality reduction techniques for multicriteria shortest path problems, enhancing speed and memory efficiency.

Findings

Achieves at least 6x speedup on simple criteria

Up to 60x speedup on complex instances

Reduces memory requirements by up to 13 times

Abstract

This paper introduces a novel algorithm combination designed for fast one-to-many multicriteria shortest path search. A preprocessing algorithm excludes irrelevant vertices by building a smaller cover graph. A modified version of multicriteria label-setting algorithm operates on the cover graph and employs a dimensionality reduction technique for swifter domination checks. While the method itself maintains solution optimality, it is able to additionally incorporate existing heuristics for further speedups. The proposed algorithm has been tested on multiple criteria combinations of varying correlation. The results show the introduced approach provides a speedup of at least 6 times on simple criteria combinations and up to 60 times on hard instances compared to vanilla multicriteria label-setting. Graph preprocessing also decreases memory requirements of queries by up to 13 times.