ABSTRACT
Online navigation platforms are well optimized to solve the standard objective of minimizing travel time and typically require precomputation-based architectures (such as Contraction Hierarchies and Customizable Route Planning) to do so in a fast manner. The reason for this dependence is the size of the graph that represents the road network, which is large. The need to go beyond minimizing the travel time and introduce various types of customizations has led to approaches that rely on alternative route computation or, more generally, small subgraph extraction. On a small subgraph, one can run computationally expensive algorithms at query time and compute optimal solutions for multiple routing problems. In this framework, it is critical for the subgraph to (a) be small and (b) include (near) optimal routes for a collection of customizations. This is precisely the setting that we study in this work. We design algorithms that extract a subgraph connecting designated terminals with the objective of minimizing the subgraph's size and the constraint of including near-optimal routes for a set of predefined cost functions. We provide theoretical guarantees for our algorithms and evaluate them empirically using real-world road networks.
Supplemental Material
- Ittai Abraham, Daniel Delling, Andrew V. Goldberg, and Renato F. Werneck. 2013. Alternative routes in road networks. ACM J. Exp. Algorithmics , Vol. 18 (2013).Google Scholar
- Roland Bader, Jonathan Dees, Robert Geisberger, and Peter Sanders. 2011. Alternative Route Graphs in Road Networks. In Theory and Practice of Algorithms in (Computer) Systems, Alberto Marchetti-Spaccamela and Michael Segal (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg, 21--32.Google Scholar
- M Ben-Akiva, M J Bergman, Andrew J Daly, and Rohit Ramaswamy. 1984. Modeling inter-urban route choice behaviour. In International Symposium on Transportation and Traffic Theory. VNU Press, 299--330.Google Scholar
- Victoria G. Crawford, Alan Kuhnle, and My T. Thai. 2019. Submodular Cost Submodular Cover with an Approximate Oracle. In Proceedings of the 36th International Conference on Machine Learning, ICML 2019, 9--15 June 2019, Long Beach, California, USA (Proceedings of Machine Learning Research, Vol. 97), , Kamalika Chaudhuri and Ruslan Salakhutdinov (Eds.). PMLR, 1426--1435. http://proceedings.mlr.press/v97/crawford19a.htmlGoogle Scholar
- Daniel Delling, Andrew V. Goldberg, Thomas Pajor, and Renato F. Werneck. 2017. Customizable Route Planning in Road Networks. Transp. Sci. , Vol. 51, 2 (2017), 566--591.Google ScholarCross Ref
- Daniel Delling, Andrew V. Goldberg, Ilya P. Razenshteyn, and Renato Fonseca F. Werneck. 2011. Graph Partitioning with Natural Cuts. In 25th IEEE International Symposium on Parallel and Distributed Processing, IPDPS 2011, Anchorage, Alaska, USA, 16--20 May, 2011 - Conference Proceedings. IEEE, 1135--1146.Google ScholarDigital Library
- Burak Eksioglu, Arif Volkan Vural, and Arnold Reisman. 2009. The vehicle routing problem: A taxonomic review. Computers & Industrial Engineering , Vol. 57, 4 (2009), 1472--1483. https://doi.org/10.1016/j.cie.2009.05.009Google ScholarDigital Library
- Zachary Friggstad, Sreenivas Gollapudi, Kostas Kollias, Tamá s Sarló s, Chaitanya Swamy, and Andrew Tomkins. 2018. Orienteering Algorithms for Generating Travel Itineraries. In Proceedings of the Eleventh ACM International Conference on Web Search and Data Mining, WSDM 2018, Marina Del Rey, CA, USA, February 5--9, 2019, , Yi Chang, Chengxiang Zhai, Yan Liu, and Yoelle Maarek (Eds.). ACM, 180--188. https://doi.org/10.1145/3159652.3159697Google ScholarDigital Library
- Robert Geisberger, Peter Sanders, Dominik Schultes, and Christian Vetter. 2012. Exact Routing in Large Road Networks Using Contraction Hierarchies. Transportation Science , Vol. 46, 3 (Aug. 2012), 388--404.Google ScholarDigital Library
- Rishabh K. Iyer and Jeff A. Bilmes. 2013. Submodular Optimization with Submodular Cover and Submodular Knapsack Constraints. In Advances in Neural Information Processing Systems 26: 27th Annual Conference on Neural Information Processing Systems 2013. Proceedings of a meeting held December 5--8, 2013, Lake Tahoe, Nevada, United States, , Christopher J. C. Burges, Lé on Bottou, Zoubin Ghahramani, and Kilian Q. Weinberger (Eds.). 2436--2444. https://proceedings.neurips.cc/paper/2013/hash/a1d50185e7426cbb0acad1e6ca74b9aa-Abstract.htmlGoogle Scholar
- Richard M. Karp. 1972. Reducibility among Combinatorial Problems. Springer US, Boston, MA, 85--103. https://doi.org/10.1007/978--1--4684--2001--2_9Google ScholarCross Ref
- Moritz Kobitzsch, Marcel Radermacher, and Dennis Schieferdecker. 2013. Evolution and Evaluation of the Penalty Method for Alternative Graphs. In 13th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems, ATMOS 2013, September 5, 2013, Sophia Antipolis, France (OASICS, Vol. 33), , Daniele Frigioni and Sebastian Stiller (Eds.). Schloss Dagstuhl - Leibniz-Zentrum fü r Informatik, 94--107.Google Scholar
- Dennis Luxen and Dennis Schieferdecker. 2012. Candidate Sets for Alternative Routes in Road Networks. In Experimental Algorithms - 11th International Symposium, SEA 2012, Bordeaux, France, June 7--9, 2012. Proceedings (Lecture Notes in Computer Science, Vol. 7276), Ralf Klasing (Ed.). Springer, 260--270.Google Scholar
- OpenStreetMap contributors. 2017. Planet dump retrieved from https://planet.osm.org . https://www.openstreetmap.org.Google Scholar
- Andreas Paraskevopoulos and Christos D. Zaroliagis. 2013. Improved Alternative Route Planning. In 13th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems, ATMOS 2013, September 5, 2013, Sophia Antipolis, France (OASICS, Vol. 33), Daniele Frigioni and Sebastian Stiller (Eds.). Schloss Dagstuhl - Leibniz-Zentrum fü r Informatik, 108--122.Google Scholar
- Ran Raz and Shmuel Safra. 1997. A Sub-Constant Error-Probability Low-Degree Test, and a Sub-Constant Error-Probability PCP Characterization of NP. In Proceedings of the Twenty-Ninth Annual ACM Symposium on the Theory of Computing, El Paso, Texas, USA, May 4--6, 1997, , Frank Thomson Leighton and Peter W. Shor (Eds.). ACM, 475--484. https://doi.org/10.1145/258533.258641Google ScholarDigital Library
- Ali Kemal Sinop, Lisa Fawcett, Sreenivas Gollapudi, and Kostas Kollias. 2021. Robust Routing Using Electrical Flows. In SIGSPATIAL '21: 29th International Conference on Advances in Geographic Information Systems, Virtual Event / Beijing, China, November 2--5, 2021, Xiaofeng Meng, Fusheng Wang, Chang-Tien Lu, Yan Huang, Shashi Shekhar, and Xing Xie (Eds.). ACM, 282--292.Google Scholar
- Tasuku Soma and Yuichi Yoshida. 2015. A Generalization of Submodular Cover via the Diminishing Return Property on the Integer Lattice. In Advances in Neural Information Processing Systems 28: Annual Conference on Neural Information Processing Systems 2015, December 7--12, 2015, Montreal, Quebec, Canada, , Corinna Cortes, Neil D. Lawrence, Daniel D. Lee, Masashi Sugiyama, and Roman Garnett (Eds.). 847--855. https://proceedings.neurips.cc/paper/2015/hash/7bcdf75ad237b8e02e301f4091fb6bc8-Abstract.htmlGoogle Scholar
- Peng-Jun Wan, Ding-Zhu Du, Panos M. Pardalos, and Weili Wu. 2010. Greedy approximations for minimum submodular cover with submodular cost. Comput. Optim. Appl. , Vol. 45, 2 (2010), 463--474. https://doi.org/10.1007/s10589-009--9269-yGoogle ScholarDigital Library
- Laurence A. Wolsey. 1982. An analysis of the greedy algorithm for the submodular set covering problem. Comb. , Vol. 2, 4 (1982), 385--393. https://doi.org/10.1007/BF02579435Google ScholarCross Ref
- Jin Y. Yen. 1971. Finding the K Shortest Loopless Paths in a Network. Management Science, Vol. 17, 11 (1971), 712--716. ioGoogle ScholarDigital Library
Index Terms
- Extracting Small Subgraphs in Road Networks
Recommendations
Complete bipartite graphs without small rainbow subgraphs
AbstractMotivated by bipartite Gallai–Ramsey type problems, we consider edge-colorings of complete bipartite graphs without rainbow tree and matching. Given two graphs G and H, and a positive integer k, define the bipartite Gallai–Ramsey number bgr k ( G ...
Forbidden Subgraphs and Weak Locally Connected Graphs
A graph is called H-free if it has no induced subgraph isomorphic to H. A graph is called $$N^i$$Ni-locally connected if $$G[\{ x\in V(G): 1\le d_G(w, x)\le i\}]$$G[{x?V(G):1≤dG(w,x)≤i}] is connected and $$N_2$$N2-locally connected if $$G[\{uv: \{uw, vw\...
A tight bound on the collection of edges in MSTs of induced subgraphs
Let G=(V,E) be a complete n-vertex graph with distinct positive edge weights. We prove that for k@?{1,2,...,n-1}, the set consisting of the edges of all minimum spanning trees (MSTs) over induced subgraphs of G with n-k+1 vertices has at most nk-(k+12) ...
Comments