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Hierarchical Cut Labelling - Scaling Up Distance Queries on Road Networks

Published: 12 December 2023 Publication History

Abstract

Answering the shortest-path distance between two arbitrary locations is a fundamental problem in road networks. Labelling-based solutions are the current state-of-the-arts to render fast response time, which can generally be categorised into hub-based labellings, highway-based labellings, and tree decomposition labellings. Hub-based and highway-based labellings exploit hierarchical structures of road networks with the aim to reduce labelling size for improving query efficiency. However, these solutions still result in large search spaces on distance labels at query time, particularly when road networks are large. Tree decomposition labellings leverage a hierarchy of vertices to reduce search spaces over distance labels at query time, but such a hierarchy is generated using tree decomposition techniques, which may yield very large labelling sizes and slow querying. In this paper, we propose a novel solution hierarchical cut 2-hop labelling (HC2L) to address the drawbacks of the existing works. Our solution combines the benefits of hierarchical structures from both perspectives - reduce the size of a distance labelling at preprocessing time and further reduce the search space on a distance labelling at query time. At its core, we propose a new hierarchy, balanced tree hierarchy, which enables a fast, efficient data structure to reduce the size of distance labelling and to select a very small subset of labels to compute the shortest-path distance at query time. To speed up the construction process of HC2L, we further propose a parallel variant of our method, namely HC2L^p. We have evaluated our solution on 10 large real-world road networks through extensive experiments. The results show that our method is 1.5-4 times faster in terms of query processing while being comparable in terms of labelling construction time and achieving up to 60% smaller labelling size compared to the state-of-the-art approaches.

References

[1]
Ittai Abraham, Daniel Delling, Andrew V. Goldberg, and Renato F. Werneck. 2011. A Hub-Based Labeling Algorithm for Shortest Paths in Road Networks. In Proceedings of the 10th International Conference on Experimental Algorithms. 230--241.
[2]
Ittai Abraham, Daniel Delling, Andrew V. Goldberg, and Renato F. Werneck. 2012. Hierarchical Hub Labelings for Shortest Paths. In Proceedings of the 20th Annual European Conference on Algorithms. 24--35.
[3]
PTV AG. [n. d.]. Western europe dataset. http://www.ptv.de
[4]
Takuya Akiba, Yoichi Iwata, Ken-ichi Kawarabayashi, and Yuki Kawata. 2014. Fast shortest-path distance queries on road networks by pruned highway labeling. In Proceedings of the 16th workshop on algorithm engineering and experiments (ALENEX). 147--154.
[5]
Takuya Akiba, Yoichi Iwata, and Yuichi Yoshida. 2013. Fast exact shortest-path distance queries on large networks by pruned landmark labeling. In Proceedings of the 2013 ACM SIGMOD International Conference on Management of Data. 349--360.
[6]
Stefan Arnborg, Derek G Corneil, and Andrzej Proskurowski. 1987. Complexity of finding embeddings in ak-tree. SIAM Journal on Algebraic Discrete Methods 8, 2 (1987), 277--284.
[7]
Julian Arz, Dennis Luxen, and Peter Sanders. 2013. Transit node routing reconsidered. In Proceedings of the 12th International Symposium on Experimental Algorithms. 55--66.
[8]
Maxim Babenko, Andrew V Goldberg, Haim Kaplan, Ruslan Savchenko, and Mathias Weller. 2015. On the complexity of hub labeling. In 40th International Symposium Mathematical Foundations of Computer Science (MFCS). 62--74.
[9]
Holger Bast, Stefan Funke, and Domagoj Matijevic. 2006. Transit ultrafast shortest-path queries with linear-time preprocessing. 9th DIMACS Implementation Challenge [1] (2006).
[10]
Michael A. Bender and Martín Farach-Colton. 2000. The LCA Problem Revisited. In LATIN 2000: Theoretical Informatics, Gaston H. Gonnet and Alfredo Viola (Eds.). Springer Berlin Heidelberg, 88--94.
[11]
Hans L. Bodlaender. 1993. A Tourist Guide through Treewidth. Acta Cybern. 11, 1--2 (1993), 1--21.
[12]
Hans L Bodlaender. 2006. Treewidth: characterizations, applications, and computations. In Graph-Theoretic Concepts in Computer Science: 32nd International Workshop. Springer, 1--14.
[13]
J. A. Bondy and U. S. R. Murty. 1976. Graph Theory with Applications. Elsevier.
[14]
Zitong Chen, Ada Wai-Chee Fu, Minhao Jiang, Eric Lo, and Pengfei Zhang. 2021. P2h: Efficient distance querying on road networks by projected vertex separators. In Proceedings of the 2021 ACM SIGMOD International Conference on Management of Data. 313--325.
[15]
Edith Cohen, Eran Halperin, Haim Kaplan, and Uri Zwick. 2003. Reachability and distance queries via 2-hop labels. SIAM J. Comput. 32, 5 (2003), 1338--1355.
[16]
Camil Demetrescu, Andrew V Goldberg, and David S Johnson. 2009. The shortest path problem: Ninth DIMACS implementation challenge. Vol. 74. American Mathematical Society.
[17]
Yefim Dinitz. 2006. Dinitz' Algorithm: The Original Version and Even's Version. In Theoretical Computer Science, Essays in Memory of Shimon Even (Lecture Notes in Computer Science, Vol. 3895), Oded Goldreich, Arnold L. Rosenberg, and Alan L. Selman (Eds.). 218--240.
[18]
DongKai Fan and Ping Shi. 2010. Improvement of Dijkstra's algorithm and its application in route planning. In Proceedings of the 7th international conference on fuzzy systems and knowledge discovery, Vol. 4. 1901--1904.
[19]
Uriel Feige and Mohammad Mahdian. 2006. Finding small balanced separators. In Proceedings of the 38th Annual ACM Symposium on Theory of Computing, Jon M. Kleinberg (Ed.). 375--384.
[20]
Cyril Gavoille, David Peleg, Stéphane Pérennes, and Ran Raz. 2004. Distance labeling in graphs. Journal of Algorithms 53, 1 (2004), 85--112.
[21]
Robert Geisberger, Peter Sanders, Dominik Schultes, and Daniel Delling. 2008. Contraction hierarchies: Faster and simpler hierarchical routing in road networks. In International Workshop on Experimental and Efficient Algorithms. 319--333.
[22]
Andrew V Goldberg and Chris Harrelson. 2005. Computing the shortest path: A search meets graph theory. In ACM-SIAM Symposium on Discrete Algorithms (SODA), Vol. 5. 156--165.
[23]
Ronald J Gutman. 2004. Reach-Based Routing: A New Approach to Shortest Path Algorithms Optimized for Road Networks. Proceedings of the Sixth Workshop on Algorithm Engineering and Experiments and the First Workshop on Analytic Algorithmics and Combinatorics (ALENEX/ANALC) 4 (2004), 100--111.
[24]
Shuai Huang, Yong Wang, Tianyu Zhao, and Guoliang Li. 2021. A learning-based method for computing shortest path distances on road networks. In Proceedings of the 37th IEEE International Conference on Data Engineering (ICDE). 360--371.
[25]
Ruoming Jin, Ning Ruan, Yang Xiang, and Victor Lee. 2012. A highway-centric labeling approach for answering distance queries on large sparse graphs. In Proceedings of the 2012 ACM SIGMOD International Conference on Management of Data. 445--456.
[26]
Sungwon Jung and Sakti Pramanik. 2002. An efficient path computation model for hierarchically structured topographical road maps. IEEE Transactions on Knowledge and Data Engineering 14, 5 (2002), 1029--1046.
[27]
Hans-Peter Kriegel, Peer Kröger, Peter Kunath, Matthias Renz, and Tim Schmidt. 2007. Proximity queries in large traffic networks. In Proceedings of the 15th annual ACM international symposium on Advances in geographic information systems. 1--8.
[28]
Dian Ouyang, Lu Qin, Lijun Chang, Xuemin Lin, Ying Zhang, and Qing Zhu. 2018. When hierarchy meets 2-hoplabeling: Efficient shortest distance queries on road networks. In Proceedings of the 2018 ACM SIGMOD International Conference on Management of Data. 709--724.
[29]
Ira Sheldon Pohl. 1969. Bi-Directional and Heuristic Search in Path Problems. Ph.D. Dissertation. Stanford, CA, USA.
[30]
Peter Sanders and Dominik Schultes. 2005. Highway Hierarchies Hasten Exact Shortest Path Queries. In Proceedings of the 13th Annual European Conference on Algorithms. 568--579.
[31]
Robert Endre Tarjan. 1983. Data structures and network algorithms. SIAM.
[32]
Pranali Yawalkar and Sayan Ranu. 2019. Route recommendations on road networks for arbitrary user preference functions. In Proceedings of the 2019 IEEE 35th International Conference on Data Engineering (ICDE). 602--613.
[33]
Mengxuan Zhang. 2021. Efficient shortest path query processing in dynamic road networks. Ph.D. Dissertation.
[34]
Yikai Zhang and Jeffrey Xu Yu. 2022. Relative Subboundedness of Contraction Hierarchy and Hierarchical 2-Hop Index in Dynamic Road Networks. In Proceedings of the 2022 ACM SIGMOD International Conference on Management of Data. 1992--2005.
[35]
Bolong Zheng, Jingyi Wan, Yongyong Gao, Yong Ma, Kai Huang, Xiaofang Zhou, and Christian S. Jensen. 2022. Workload-Aware Shortest Path Distance Querying in Road Networks. In Proceedings of the 38th IEEE International Conference on Data Engineering ICDE. 2372--2384.
[36]
Andy Diwen Zhu, Hui Ma, Xiaokui Xiao, Siqiang Luo, Youze Tang, and Shuigeng Zhou. 2013. Shortest Path and Distance Queries on Road Networks: Towards Bridging Theory and Practice. In Proceedings of the 2013 ACM SIGMOD International Conference on Management of Data.

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cover image Proceedings of the ACM on Management of Data
Proceedings of the ACM on Management of Data  Volume 1, Issue 4
PACMMOD
December 2023
1317 pages
EISSN:2836-6573
DOI:10.1145/3637468
Issue’s Table of Contents
This work is licensed under a Creative Commons Attribution International 4.0 License.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 12 December 2023
Published in PACMMOD Volume 1, Issue 4

Author Tags

  1. 2-hop labelling
  2. balanced tree hierarchy
  3. distance labelling
  4. hierarchical partitioning
  5. road network
  6. shortest-path distance
  7. vertex cut

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