Customizable Hub Labeling: Properties and Algorithms

TL;DR

This paper introduces a customizable variant of Hub Labeling for route planning that allows labels to be adapted to different edge costs after preprocessing, supported by theoretical analysis and efficient algorithms.

Contribution

It proposes a new customizable hub labeling method that decouples preprocessing from edge costs, with theoretical guarantees and practical algorithms for customization.

Findings

Provides an $ ext{O}( ext{log}^2 n)$-approximation algorithm for label size

Develops efficient algorithms for label customization

Analyzes theoretical properties of customizable hub labelings

Abstract

Hub Labeling (HL) is one of the state-of-the-art preprocessing-based techniques for route planning in road networks. It is a special incarnation of distance labeling, and it is well-studied in both theory and practice. The core concept of HL is to associate a label with each vertex, which consists of a subset of all vertices and respective shortest path information, such that the shortest path distance between any two vertices can be derived from considering the intersection of their labels. HL provides excellent query times but requires a time-consuming preprocessing phase. Therefore, in case of edge cost changes, rerunning the whole preprocessing is not viable. Inspired by the concept of Customizable Route Planning, we hence propose in this paper a Customizable Hub Labeling variant for which the edge costs in the network do not need to be known at construction time. These labels can then be used with any edge costs after conducting a so called customization phase. We study the theoretical properties of Customizable Hub Labelings, provide an $\mathcal{O}(\log^2 n)$-approximation algorithm for the average label size, and propose efficient customization algorithms.