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Exact and Approximate Hierarchical Hub Labeling

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UEHARA, Ryuhei, ed., Katsuhisa YAMANAKA, ed., Hsu-Chun YEN, ed.. WALCOM: Algorithms and Computation : 18th International Conference and Workshops on Algorithms and Computation, WALCOM 2024, Kanazawa, Japan, March 18–20, 2024, Proceedings. Singapore: Springer, 2024, pp. 194-211. Lecture Notes in Computer Science (LNCS). 14549. ISSN 0302-9743. eISSN 1611-3349. ISBN 978-981-9705-65-8. Available under: doi: 10.1007/978-981-97-0566-5_15

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Hub Labeling (HL) is a state-of-the-art technique for accelerating shortest path computation in road networks. By utilizing precomputed node labels, it can answer distance queries in microseconds on continent-sized networks. The optimization goal is to get correct query results with a minimum number of labels. There is an O(log n) approximation algorithm for the size of an HL with a running time of O(n3 log n). However, existing practical implementations rely mostly on heuristics for a special type of HL, so called Hierarchical HL (HHL). Deciding whether a graph admits a labeling of size at most k is NP-hard for both HL and HHL. For HHL, an O(√n log n) approximation algorithm (called w-HHL) is known, as well as a parametrized upper bound of O(t log n) on the average label size, where t denotes the treewidth of the network. In this paper, we devise an exact HHL algorithm for general graphs. Furthermore, we improve the parametrized approximation factor to O (b), where b denotes the balanced separator number with b - 1 ≤ t. We also show that w-HHL provides a constant factor approximation on trees, and investigate for the first time the practical performance of existing HHL approximation algorithms. Our theoretical results offer some explanatory power for the good performance of HHL on road networks, while our experimental results show that commonly used methods for HHL are noticeably outperformed by w-HHL on general graphs as well as trees.

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WALCOM 2024 : 18th International Conference and Workshops on Algorithms and Computation, 18. März 2024 - 20. März 2024, Kanazawa, Japan
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ISO 690LI, Ruoying, Sabine STORANDT, 2024. Exact and Approximate Hierarchical Hub Labeling. WALCOM 2024 : 18th International Conference and Workshops on Algorithms and Computation. Kanazawa, Japan, 18. März 2024 - 20. März 2024. In: UEHARA, Ryuhei, ed., Katsuhisa YAMANAKA, ed., Hsu-Chun YEN, ed.. WALCOM: Algorithms and Computation : 18th International Conference and Workshops on Algorithms and Computation, WALCOM 2024, Kanazawa, Japan, March 18–20, 2024, Proceedings. Singapore: Springer, 2024, pp. 194-211. Lecture Notes in Computer Science (LNCS). 14549. ISSN 0302-9743. eISSN 1611-3349. ISBN 978-981-9705-65-8. Available under: doi: 10.1007/978-981-97-0566-5_15
BibTex
@inproceedings{Li2024Exact-69921,
  year={2024},
  doi={10.1007/978-981-97-0566-5_15},
  title={Exact and Approximate Hierarchical Hub Labeling},
  number={14549},
  isbn={978-981-9705-65-8},
  issn={0302-9743},
  publisher={Springer},
  address={Singapore},
  series={Lecture Notes in Computer Science (LNCS)},
  booktitle={WALCOM: Algorithms and Computation : 18th International Conference and Workshops on Algorithms and Computation, WALCOM 2024, Kanazawa, Japan, March 18–20, 2024, Proceedings},
  pages={194--211},
  editor={Uehara, Ryuhei and Yamanaka, Katsuhisa and Yen, Hsu-Chun},
  author={Li, Ruoying and Storandt, Sabine}
}
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    <dcterms:abstract>Hub Labeling (HL) is a state-of-the-art technique for accelerating shortest path computation in road networks. By utilizing precomputed node labels, it can answer distance queries in microseconds on continent-sized networks. The optimization goal is to get correct query results with a minimum number of labels. There is an O(log n) approximation algorithm for the size of an HL with a running time of O(n&lt;sup&gt;3&lt;/sup&gt; log n). However, existing practical implementations rely mostly on heuristics for a special type of HL, so called Hierarchical HL (HHL). Deciding whether a graph admits a labeling of size at most k is NP-hard for both HL and HHL. For HHL, an O(√n log n)  approximation algorithm (called w-HHL) is known, as well as a parametrized upper bound of O(t log n) on the average label size, where t denotes the treewidth of the network. In this paper, we devise an exact HHL algorithm for general graphs. Furthermore, we improve the parametrized approximation factor to O (b), where b denotes the balanced separator number with b - 1 ≤ t. We also show that w-HHL provides a constant factor approximation on trees, and investigate for the first time the practical performance of existing HHL approximation algorithms. Our theoretical results offer some explanatory power for the good performance of HHL on road networks, while our experimental results show that commonly used methods for HHL are noticeably outperformed by w-HHL on general graphs as well as trees.</dcterms:abstract>
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