On the Complexity of Hub Labeling (Extended Abstract)
- Cite this paper as:
- Babenko M., Goldberg A.V., Kaplan H., Savchenko R., Weller M. (2015) On the Complexity of Hub Labeling (Extended Abstract). In: Italiano G., Pighizzini G., Sannella D. (eds) Mathematical Foundations of Computer Science 2015. MFCS 2015. Lecture Notes in Computer Science, vol 9235. Springer, Berlin, Heidelberg
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.