Hierarchical Multicriteria Shortest Path Search

TL;DR

This work tackles multicriteria shortest-path search, especially under time-dependent metrics, by introducing Hierarchical MLS, a label-setting algorithm that operates on a hierarchy of nested $k$-Path-Cover graphs. The method builds $G_t$ covers with $k=2^p$ and uses a two-stage search (backward to the top level, then forward on the top level) augmented with lexicographic label ordering and dimensionality reduction via $t$-discarding. Key contributions include a scalable preprocessing phase, compatibility with existing pruning techniques, and substantial empirical speedups and memory savings on road-network and DIMACS benchmarks. The results demonstrate that Hierarchical MLS can outperform direct MLS approaches by large factors, enabling efficient optimal multicriteria routing in dynamic settings.

Abstract

This paper presents a novel multicriteria shortest path search algorithm called Hierarchical MLS. The distinguishing feature of the algorithm is the multilayered structure of compressed k-Path-Cover graphs it operates on. In addition to providing significant improvements in terms of time and memory consumption, the algorithm is notable for several other features. Due to the preprocessing phase requiring only several seconds, the algorithm can be successfully applied to scenarios with dynamic prices. Moreover, the algorithm does not employ bidirectional search, and can thus work on time-dependent metrics. We test the algorithm on multiple graphs and analyze its performance in terms of time and memory efficiency. The results prove Hierarchical MLS to be faster than its direct alternatives by at least 2 times in terms of query runtime and at least 20 times in terms of preprocessing.

Figures (3)

• Figure 1: Cumulative construction times of hierarchical covers
• Figure 2: Number of vertices of hierarchical covers
• Figure 3: Number of edges of hierarchical covers