Online Routing in Triangulations
Abstract
We consider online routing algorithms for routing between the vertices of embedded planar straight line graphs. Our results include (1) two deterministic memoryless routing algorithms, one that works for all Delaunay triangulations and the other that works for all regular triangulations; (2) a randomized memoryless algorithm that works for all triangulations; (3) an O(1) memory algorithm that works for all convex subdivisions; (4) an O(1) memory algorithm that approximates the shortest path in Delaunay triangulations; and (5) theoretical and experimental results on the competitiveness of these algorithms.
MSC codes
Keywords
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Ricardo Baeza‐Yates, Joseph Culberson, Gregory Rawlins, Searching in the plane, Inform. and Comput., 106 (1993), 234–252
2.
J. Bondy, U. Murty, Graph theory with applications, American Elsevier Publishing Co., Inc., New York, 1976x + 264
3.
Allan Borodin, Ran El‐Yaniv, Online computation and competitive analysis, Cambridge University Press, 1998xviii+414
4.
P. Bose, P. Morin, I. Stojmenović, and J. Urrutia, Routing with guaranteed delivery in ad hoc wireless networks, in Proceedings of Discrete Algorithms and Methods for Mobility (DIALM’99), ACM, New York, 1999, pp. 48–55.
5.
V. Chvátal, A combinatorial theorem in plane geometry, J. Combinatorial Theory Ser. B, 18 (1975), 39–41
6.
M. de Berg, M. van Kreveld, R. van Oostrum, and M. Overmars, Simple traversal of a subdivision without extra storage, Internat. J. Geographic Inform. Systems, 11 (1997), pp. 359–373.
7.
David Dobkin, Steven Friedman, Kenneth Supowit, Delaunay graphs are almost as good as complete graphs, Discrete Comput. Geom., 5 (1990), 399–407
8.
H. Edelsbrunner, An acyclicity theorem for cell complexes in dimension, Combinatorica, 10 (1990), 251–260
9.
Subir Ghosh, Sanjeev Saluja, Optimal on‐line algorithms for walking with minimum number of turns in unknown streets, Comput. Geom., 8 (1997), 241–266
10.
C. Icking and R. Klein, Searching for the kernel of a polygon: A competitive strategy, in Proceedings of the 11th Annual ACM Symposium on Computational Geometry, ACM, New York, 1995, pp. 258–266.
11.
J. Keil, Carl Gutwin, Classes of graphs which approximate the complete Euclidean graph, Discrete Comput. Geom., 7 (1992), 13–28
12.
Rolf Klein, Walking an unknown street with bounded detour, Comput. Geom., 1 (1992), 325–351
13.
E. Kranakis, H. Singh, and J. Urrutia, Compass routing on geometric networks, in Proceedings of the 11th Canadian Conference on Computational Geometry (CCCG’99), 1999, pp. 51–54;
available online from http://www.cccg.ca/proceedings/1999/.
14.
C. L. Lawson, Software for surface interpolation, in Mathematical Software III, Academic Press, New York, 1977, pp. 161–194.
15.
X. Lin and I. Stojmenović, Geographic Distance Routing in Ad Hoc Wireless Networks, Tech. Report TR‐98‐10, SITE, University of Ottawa, Canada, 1998.
16.
Atsuyuki Okabe, Barry Boots, Kōkichi Sugihara, Spatial tessellations: concepts and applications of Vorono diagrams, Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics, John Wiley & Sons Ltd., 1992xii+532, With a foreword by D. G. Kendall
17.
Franco Preparata, Michael Shamos, Computational geometry, Texts and Monographs in Computer Science, Springer‐Verlag, 1985xii+390, An introduction
18.
Günter Ziegler, Lectures on polytopes, Graduate Texts in Mathematics, Vol. 152, Springer‐Verlag, 1995x+370
Information & Authors
Information
Published In
SIAM Journal on Computing
Pages: 937 - 951
ISSN (online): 1095-7111
Copyright
Copyright © 2004 Society for Industrial and Applied Mathematics.
History
Published online: 17 February 2012
MSC codes
Keywords
Authors
Metrics & Citations
Metrics
Citations
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.
Cited By
- Routing on heavy path WSPD spannersComputational Geometry, Vol. 123 | 1 Dec 2024
- Frisbee: An Efficient Data Sharing Framework for UAV SwarmsIEEE Transactions on Network Science and Engineering, Vol. 11, No. 6 | 1 Nov 2024
- On the Spanning and Routing Ratio of the Directed Theta-Four GraphDiscrete & Computational Geometry, Vol. 71, No. 3 | 6 October 2023
- Evaluation of Road Network Effectiveness with Rank-Based Random Walk2024 18th International Conference on Ubiquitous Information Management and Communication (IMCOM) | 3 Jan 2024
- A Survey on Rerouting Techniques with P4 Programmable Data Plane SwitchesComputer Networks, Vol. 230 | 1 Jul 2023
- On the spanning and routing ratios of the directed Θ6-graphComputational Geometry, Vol. 105-106 | 1 Aug 2022
- Defending Trace-Back Attack in 3D Wireless Internet of ThingsIEEE/ACM Transactions on Networking, Vol. 30, No. 4 | 1 Aug 2022
- A robust fast bridging algorithm for laser cuttingThe International Journal of Advanced Manufacturing Technology, Vol. 121, No. 3-4 | 7 June 2022
- An incremental algorithm for simultaneous construction of 2D Voronoi diagram and Delaunay triangulation based on a face-based data structureAdvances in Engineering Software, Vol. 169 | 1 Jul 2022
- Local Routing in Sparse and Lightweight Geometric GraphsAlgorithmica, Vol. 84, No. 5 | 25 January 2022
- COIN: An Efficient Indexing Mechanism for Unstructured Data Sharing SystemsIEEE/ACM Transactions on Networking, Vol. 30, No. 1 | 1 Feb 2022
- On Landmark Distances in PolygonsComputer Graphics Forum, Vol. 40, No. 5 | 23 August 2021
- On the Spanning and Routing Ratios of the Directed $$\varTheta _6$$-GraphAlgorithms and Data Structures | 31 July 2021
- Routing on Heavy-Path WSPD-SpannersAlgorithms and Data Structures | 31 July 2021
- A new memoryless online routing algorithm for Delaunay triangulations2020 10th International Conference on Computer and Knowledge Engineering (ICCKE) | 29 Oct 2020
- Local Routing in Convex SubdivisionsInternational Journal of Computational Geometry & Applications, Vol. 30, No. 01 | 31 August 2020
- A Distributed Position-Based Routing Algorithm in 3-D Wireless Industrial Internet of ThingsIEEE Transactions on Industrial Informatics, Vol. 15, No. 10 | 1 Oct 2019
- Efficient Indexing Mechanism for Unstructured Data Sharing Systems in Edge ComputingIEEE INFOCOM 2019 - IEEE Conference on Computer Communications | 1 Apr 2019
- Walking in a Planar Poisson–Delaunay Triangulation: Shortcuts in the Voronoi PathInternational Journal of Computational Geometry & Applications, Vol. 28, No. 03 | 15 November 2018
- Efficient Path Generation with Reduced CoordinatesComputer Graphics Forum, Vol. 37, No. 5 | 8 August 2018
- On the performance of greedy forwarding on Yao and Theta graphsJournal of Parallel and Distributed Computing, Vol. 117 | 1 Jul 2018
- A general framework for searching on a lineTheoretical Computer Science, Vol. 703 | 1 Dec 2017
- Competitive Online Routing on Delaunay TriangulationsInternational Journal of Computational Geometry & Applications, Vol. 27, No. 04 | 19 February 2018
- Upper and Lower Bounds for Online Routing on Delaunay TriangulationsDiscrete & Computational Geometry, Vol. 58, No. 2 | 22 November 2016
- Local Routing in Spanners Based on WSPDsAlgorithms and Data Structures | 5 July 2017
- Efficiently navigating a random Delaunay triangulationRandom Structures & Algorithms, Vol. 49, No. 1 | 24 February 2016
- A Scalable and Resilient Layer-2 Network With Ethernet CompatibilityIEEE/ACM Transactions on Networking, Vol. 24, No. 1 | 1 Feb 2016
- Planar Geometric SpannersEncyclopedia of Algorithms | 22 April 2016
- A General Framework for Searching on a LineWALCOM: Algorithms and Computation | 1 Jan 2016
- Recoverable DTN Routing Based on a Relay of Cyclic Message-Ferries on a MSQ Network2015 IEEE International Conference on Self-Adaptive and Self-Organizing Systems Workshops | 1 Sep 2015
- Greedy zone routing: Scalable routing in large scale wireless ad-hoc networks2015 12th Annual IEEE International Conference on Sensing, Communication, and Networking (SECON) | 1 Jun 2015
- A Dilution-matching-encoding compaction of trajectories over road networksGeoInformatica, Vol. 19, No. 2 | 14 September 2014
- Optimal Local Routing on Delaunay Triangulations Defined by Empty Equilateral TrianglesSIAM Journal on Computing, Vol. 44, No. 6 | 3 November 2015
- Local Routing in Convex SubdivisionsSOFSEM 2015: Theory and Practice of Computer Science | 1 Jan 2015
- Upper and Lower Bounds for Online Routing on Delaunay TriangulationsAlgorithms - ESA 2015 | 12 November 2015
- How well do Yao graph and theta graph support Greedy forwarding?2014 IEEE Global Communications Conference | 1 Dec 2014
- Cluster-Based Online Routing Protocols for Ad Hoc NetworkInternational Journal of Information Technology and Web Engineering, Vol. 9, No. 4 | 1 Oct 2014
- SIGACT news online algorithms column 24ACM SIGACT News, Vol. 45, No. 3 | 17 September 2014
- Bounded stretch geographic homotopic routing in sensor networksIEEE INFOCOM 2014 - IEEE Conference on Computer Communications | 1 Apr 2014
- Competitive Online Routing on Delaunay TriangulationsAlgorithm Theory – SWAT 2014 | 1 Jan 2014
- A Unified View to Greedy Geometric Routing Algorithms in Ad Hoc NetworksIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Vol. E97.A, No. 6 | 1 Jan 2014
- Geometric spanners: Recent results and open directions2013 Third International Conference on Communications and Information Technology (ICCIT) | 1 Jun 2013
- Geographic Routing in $d$-Dimensional Spaces With Guaranteed Delivery and Low StretchIEEE/ACM Transactions on Networking, Vol. 21, No. 2 | 1 Apr 2013
- Bounding the locality of distributed routing algorithmsDistributed Computing, Vol. 26, No. 1 | 11 September 2012
- A Unified View to Greedy Geometric Routing Algorithms in Ad Hoc NetworksAlgorithms for Sensor Systems | 1 Jan 2013
- Self-approaching GraphsGraph Drawing | 1 Jan 2013
- Compact Representation of GPS Trajectories over Vectorial Road NetworksAdvances in Spatial and Temporal Databases | 1 Jan 2013
- IMPROVING SHORTEST PATHS IN THE DELAUNAY TRIANGULATIONInternational Journal of Computational Geometry & Applications, Vol. 22, No. 06 | 3 April 2013
- Towards higher-dimensional topological self-stabilization: A distributed algorithm for Delaunay graphsTheoretical Computer Science, Vol. 457 | 1 Oct 2012
- ROME: Routing on metropolitan-scale Ethernet2012 20th IEEE International Conference on Network Protocols (ICNP) | 1 Oct 2012
- New Memoryless Online Routing Algorithms for Delaunay TriangulationsIEEE Transactions on Parallel and Distributed Systems, Vol. 23, No. 8 | 1 Aug 2012
- On graphs supporting greedy forwarding for directional wireless networks2012 IEEE International Conference on Communications (ICC) | 1 Jun 2012
- Memoryless routing in convex subdivisions: Random walks are optimalComputational Geometry, Vol. 45, No. 4 | 1 May 2012
- CSI: An Energy-Aware Cover-Sense-Inform Framework for k-Covered Wireless Sensor NetworksIEEE Transactions on Parallel and Distributed Systems, Vol. 23, No. 4 | 1 Apr 2012
- DONUT: Building Shortcuts in Large-Scale Decentralized Systems with Heterogeneous Peer Distributions2011 IEEE 30th International Symposium on Reliable Distributed Systems | 1 Oct 2011
- On a family of strong geometric spanners that admit local routing strategiesComputational Geometry, Vol. 44, No. 6-7 | 1 Aug 2011
- Minimum Weight Convex Steiner PartitionsAlgorithmica, Vol. 60, No. 3 | 12 June 2009
- Minimum power energy spanners in wireless ad hoc networksWireless Networks, Vol. 17, No. 5 | 5 May 2011
- Greedy Distance Vector Routing2011 31st International Conference on Distributed Computing Systems | 1 Jun 2011
- Forwarding via checkpoints: Geographic routing on always-on sensorsJournal of Parallel and Distributed Computing, Vol. 70, No. 7 | 1 Jul 2010
- Minimum Power Energy Spanners in Wireless Ad Hoc Networks2010 Proceedings IEEE INFOCOM | 1 Mar 2010
- Midpoint routing algorithms for Delaunay triangulations2010 IEEE International Symposium on Parallel & Distributed Processing (IPDPS) | 1 Jan 2010
- Bounding the locality of distributed routing algorithmsProceedings of the 28th ACM symposium on Principles of distributed computing | 10 August 2009
- DELAUNAY AND DIAMOND TRIANGULATIONS CONTAIN SPANNERS OF BOUNDED DEGREEInternational Journal of Computational Geometry & Applications, Vol. 19, No. 02 | 20 November 2011
- Local Construction of Near-Optimal Power Spanners for Wireless Ad Hoc NetworksIEEE Transactions on Mobile Computing, Vol. 8, No. 4 | 1 Apr 2009
- On Spanners of Geometric GraphsTheory and Applications of Models of Computation | 1 Jan 2009
- Efficient and accurate protocols for distributed delaunay triangulation under churn2008 IEEE International Conference on Network Protocols | 1 Oct 2008
- A Radius Geocast Routing Protocol2008 10th IEEE International Conference on High Performance Computing and Communications | 1 Sep 2008
- Planar Geometric SpannersEncyclopedia of Algorithms | 1 Jan 2008
- Almost Delaunay triangulation routing in wireless sensor networks2007 10th International Conference on Computer and Information Technology | 1 Dec 2007
- Improvement of the robustness on geographical networks by adding shortcutsPhysica A: Statistical Mechanics and its Applications, Vol. 380 | 1 Jul 2007
- On a Family of Strong Geometric Spanners That Admit Local Routing StrategiesAlgorithms and Data Structures | 1 Jan 2007
- Protocol Design for Dynamic Delaunay Triangulation27th International Conference on Distributed Computing Systems (ICDCS '07) | 1 Jan 2007
- Geographical effects on the path length and the robustness in complex networksPhysical Review E, Vol. 73, No. 6 | 9 June 2006
- Geographical Construction of Scale-Free Networks with Both Short Path Lengths and HopsComputational Science – ICCS 2006 | 1 Jan 2006
- Diamond Triangulations Contain Spanners of Bounded DegreeAlgorithms and Computation | 1 Jan 2006
- Online Multi-path Routing in a MazeAlgorithms and Computation | 1 Jan 2006
- Improved Stretch Factor for Bounded-Degree Planar Power Spanners of Wireless Ad-Hoc NetworksAlgorithmic Aspects of Wireless Sensor Networks | 1 Jan 2006
- Compact Routing for Graphs Excluding a Fixed MinorDistributed Computing | 1 Jan 2005
- Competitive online routing in geometric graphsTheoretical Computer Science, Vol. 324, No. 2-3 | 1 Sep 2004
View Options
- Access via your Institution
- Questions about how to access this content? Contact SIAM at [email protected].