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

  1. 65D18
  2. 90B18

Keywords

  1. routing
  2. online algorithms
  3. Delaunay triangulations
  4. shortest path
  5. spanning path

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 d 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 C1 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 Voronoi˘ 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

cover image SIAM Journal on Computing
SIAM Journal on Computing
Pages: 937 - 951
ISSN (online): 1095-7111

History

Published online: 17 February 2012

MSC codes

  1. 65D18
  2. 90B18

Keywords

  1. routing
  2. online algorithms
  3. Delaunay triangulations
  4. shortest path
  5. spanning path

Authors

Affiliations

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

View Options

View options

PDF

View PDF

Figures

Tables

Media

Share

Share

Copy the content Link

Share with email

Email a colleague

Share on social media