Robust Routing Using Electrical Flows

ABSTRACT

Generating alternative routes in road networks is an application of significant interest for online navigation systems. A high quality set of diverse alternate routes offers two functionalities - a) support multiple (unknown) preferences that the user may have; and b) robust to changes in network conditions. We address the latter in this paper. The main techniques that produce alternative routes in road networks are the penalty and the plateau methods, with the former providing high quality results but being too slow for practical use and the latter being fast but suffering in terms of quality. In this work we propose a novel method to produce alternative routes that is fundamentally different from the aforementioned approaches. Our algorithm borrows concepts from electrical flows and their decompositions. We evaluate our method against the penalty and plateau methods, showing that it is as fast as the plateau method while also recovering much of the headroom towards the quality of the penalty method. The metrics we use to evaluate performance include the stretch (the average cost of the routes), the diversity, and the robustness (the connectivity between the origin and destination) of the induced set of routes.

References

1. 2009. Camvit: Choice routing. http://www.camvit.com.
2. Ittai Abraham, Daniel Delling, Andrew V. Goldberg, and Renato F. Werneck. 2013. Alternative routes in road networks. ACM J. Exp. Algorithmics 18 (2013).
3. Gaurav Aggarwal, Sreenivas Gollapudi, Raghavender R, and Ali Kemal Sinop. 2021. Sketch-based Algorithms for Approximate Shortest Paths in Road Networks. In WWW '21: The Web Conference 2021, Ljubljana, Slovenia, April 19-23, 2021. ACM / IW3C2.
4. 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.
5. 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.
6. Michael B. Cohen, Rasmus Kyng, Gary L. Miller, Jakub W. Pachocki, Richard Peng, Anup B. Rao, and Shen Chen Xu. 2014. Solving SDD Linear Systems in Nearly m log1/2 n Time. In Proceedings of the Forty-Sixth Annual ACM Symposium on Theory of Computing (STOC '14). Association for Computing Machinery, 343--352.
7. Tomas de la Barra and B Perezand J Anez. 1993. Multidimensional path search and assignment. In PTRC Summer Annual Meeting (SAM).
8. Daniel Delling, Andrew V. Goldberg, Thomas Pajor, and Renato F. Werneck. 2017. Customizable Route Planning in Road Networks. Transp. Sci. 51, 2 (2017), 566--591.
9. 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.
10. Peter G. Doyle and J. Laurie Snell. 1984. Random walks and electric networks. Mathematical Assn of Amer.
11. David Eppstein and Michael T. Goodrich. 2008. Studying (non-planar) road networks through an algorithmic lens. In 16th ACM SIGSPATIAL International Symposium on Advances in Geographic Information Systems, ACM-GIS 2008, November 5-7, 2008, Irvine, California, USA, Proceedings, Walid G. Aref, Mohamed F. Mokbel, and Markus Schneider (Eds.). ACM, 16.
12. Christos Faloutsos, Kevin S. McCurley, and Andrew Tomkins. 2004. Fast discovery of connection subgraphs. In Proceedings of the Tenth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Seattle, Washington, USA, August 22-25, 2004, Won Kim, Ron Kohavi, Johannes Gehrke, and William DuMouchel (Eds.). ACM, 118--127.
13. Robert Geisberger, Peter Sanders, Dominik Schultes, and Christian Vetter. 2012. Exact Routing in Large Road Networks Using Contraction Hierarchies. Transportation Science 46, 3 (Aug. 2012), 388--404.
14. Prahladh Harsha, Thomas P. Hayes, Hariharan Narayanan, Harald Räcke, and Jaikumar Radhakrishnan. 2008. Minimizing average latency in oblivious routing. In Proceedings of the Nineteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2008, San Francisco, California, USA, January 20-22, 2008, Shang-Hua Teng (Ed.). SIAM, 200--207.
15. Jonathan A. Kelner and Petar Maymounkov. 2011. Electric routing and concurrent flow cutting. Theor. Comput. Sci. 412, 32 (2011), 4123--4135.
16. Moritz Kobitzsch. 2015. Alternative Route Techniques and their Applications to the Stochastics on-time Arrival Problem. Ph.D. Dissertation. Karlsruhe Institute of Technology.
17. Rasmus Kyng and Sushant Sachdeva. 2016. Approximate Gaussian Elimination for Laplacians - Fast, Sparse, and Simple. In IEEE 57th Annual Symposium on Foundations of Computer Science, FOCS 2016, 9-11 October 2016, Hyatt Regency, New Brunswick, New Jersey, USA, Irit Dinur (Ed.). IEEE Computer Society, 573--582.
18. Gregory Lawler and Hariharan Narayanan. 2009. Mixing times and lp bounds for oblivious routing. In Proceedings of the Meeting on Analytic Algorithmics and Combinatorics. Society for Industrial and Applied Mathematics, 66--74.
19. 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), Ralf Klasing (Ed.), Vol. 7276. Springer, 260--270.
20. OpenStreetMap contributors. 2017. Planet dump retrieved from https://planet.osm.org. https://www.openstreetmap.org.
21. 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), Daniele Frigioni and Sebastian Stiller (Eds.), Vol. 33. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 108--122.
22. Yousef Saad. 1996. Iterative Methods for Sparse Linear Systems. PWS Publishing Company.
23. Aaron Schild, Satish Rao, and Nikhil Srivastava. 2018. Localization of Electrical Flows. In Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018, New Orleans, LA, USA, January 7-10, 2018, Artur Czumaj (Ed.). SIAM, 1577--1584.
24. Aaron Schild and Christian Sommer. 2015. On Balanced Separators in Road Networks. In 14th International Symposium on Experimental Algorithms (SEA). 286--297.
25. Daniel A. Spielman and Shang-Hua Teng. 2004. Nearly-linear time algorithms for graph partitioning, graph sparsification, and solving linear systems. In Proceedings of the 36th Annual ACM Symposium on Theory of Computing, Chicago, IL, USA, June 13-16, 2004, László Babai (Ed.). ACM, 81--90.
26. Gilbert Strang. 1986. Introduction to Applied Mathematics. Wellesley-Cambridge Press.
27. Jin Y. Yen. 1971. Finding the K Shortest Loopless Paths in a Network. Management Science 17, 11 (1971), 712--716.

Index Terms

• Information systems

  • Information systems applications

    • Spatial-temporal systems

      • Geographic information systems

• Theory of computation

  • Design and analysis of algorithms

    • Graph algorithms analysis

      • Shortest paths