Landmark Hub Labeling : Improved Bounds and Faster Query Answering

Abstract

Hub Labeling (HL) is a state-of-the-art method for answering shortest-distance queries between node pairs in weighted graphs. It provides very fast query times but also requires considerable additional space to store the label information. Recently, a generalization of HL, called Landmark Hub Labeling (LHL), has been proposed, that conceptionally allows a storage of fewer label information without compromising the optimality of the query result. However, query answering with LHL was shown to be slower than with HL, both in theory and practice. Furthermore, it was not clear whether there are graphs with a substantial space reduction when using LHL instead of HL. In this paper, we describe a new way of storing label information of an LHL such that query times are significantly reduced and then asymptotically match those of HL. Thus, we alleviate the so far greatest shortcoming of LHL compared to HL. Moreover, we show that for the practically relevant hierarchical versions (HHL and HLHL), there are graphs in which the label size of an optimal HLHL is a factor of Θ(√ n) smaller than that of an optimal HHL. We establish further novel bounds between different labeling variants. Additionally, we provide a comparative experimental study between approximation algorithms for HL and LHL. We demonstrate that label sizes in an LHL are consistently smaller than those of HL across diverse benchmark graphs, including road networks.