Abstract
Hub Labeling (HL) is a data structure for distance oracles. Hierarchical HL (HHL) is a special type of HL, that received a lot of attention from a practical point of view. However, theoretical questions such as NP-hardness and approximation guarantees for HHL algorithms have been left aside. We study the computational complexity of HL and HHL. We prove that both HL and HHL are NP-hard, and present upper and lower bounds on the approximation ratios of greedy HHL algorithms that are used in practice. We also introduce a new variant of the greedy HHL algorithm that produces small labels for graphs with small highway dimension.
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CITATION STYLE
Babenko, M., Goldberg, A. V., Kaplan, H., Savchenko, R., & Weller, M. (2015). On the complexity of hub labeling. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9235, pp. 62–74). Springer Verlag. https://doi.org/10.1007/978-3-662-48054-0_6
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