Abstract
This paper concerns routing with succinct tables in chordal graphs. We show how to construct in polynomial time, for every n-node chordal graph of maximum clique size k, a routing scheme using routing tables of O(k log n) bits per node and O(log n) bit addresses such that the length of the route between any two nodes is at most the distance between the nodes in the graph plus two. This is complemented by a recent lower bound that shows that if the shortest paths and O(log n) bit addresses are required, every routing strategy for this class needs Ω(2k log(n/2k)) bits per node.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Stephen Alstrup and Theis Rauhe. Improved labeling scheme for ancestor queries. In 13th Symposium on Discrete Algorithms (SODA). ACM-SIAM, January 2001. To appear.
Andreas Brandstädt, Victor Chepoi, and Feodor Dragan. Distance approximating trees for chordal and dually chordal graphs. Journal of Algorithms, 30:166–184, 1999.
Andreas Brandstädt, Van Bang Le, and Jeremy P. Spinrad. Graph Classes-A survey. SIAM Monographs on Discrete Mathematics and Applications, Philadelphia, 1999.
Reinhard Diestel. Graph Theory (second edition), volume 173 of Graduate Texts in Mathematics. Springer, February 2000.
Pierre Fraigniaud and Cyril Gavoille. Routing in trees. In Fernando Orejas, Paul G. Spirakis, and Jan van Leeuwen, editors, 28 th International Colloquium on Automata, Languages and Programming (ICALP), volume 2076 of Lecture Notes in Computer Science, pages 757–772. Springer, July 2001.
Pierre Fraigniaud and Cyril Gavoille. Routing in trees. Research Report RR-1252-01, LaBRI, University of Bordeaux, 351, cours de la Libération, 33405 Talence Cedex, France, January 2001. Sumitted.
Greg N. Frederickson and Ravi Janardan. Efficient message routing in planar networks. SIAM Journal on Computing, 18(4):843–857, August 1989.
Greg N. Frederickson and Ravi Janardan. Space-efficient message routing in c-decomposable networks. SIAM Journal on Computing, 19(1):164–181, February 1990.
Cyril Gavoille. A survey on interval routing. Theoretical Computer Science, 245(2):217–253, 2000.
Cyril Gavoille. Routing in distributed networks: Overview and open problems. ACM SIGACT News-Distributed Computing Column, 32(1), March 2001. To appear.
Cyril Gavoille. Space lower bounds for routing in chordal graphs with additive stretch, 2002. In preparation.
Cyril Gavoille and Nicolas Hanusse. Compact routing tables for graphs of bounded genus. In Jiří Wiedermann, Peter van Emde Boas, and Mogens Nielsen, editors, 26th International Colloquium on Automata, Languages and Programming (ICALP), volume 1644 of Lecture Notes in Computer Science, pages 351–360. Springer, July 1999.
Cyril Gavoille and Stéphane Pérennès. Lower bounds for interval routing on 3-regular networks. In Nicola Santoro and Paul Spirakis, editors, 3rd International Colloquium on Structural Information amp; Communication Complexity (SIROCCO), pages 88–103. Carleton University Press, June 1996.
Haim Kaplan and Tova Milo. Short and simple labels for small distances and other functions. In 7th International Workshop on Algorithms and Data Structures (WADS), volume 2125 of Lecture Notes in Computer Science, pages 32–40. Springer, August 2001.
Haim Kaplan, Tova Milo, and Ronen Shabo. A comparison of labeling schemes for ancestor queries. In 14th Symposium on Discrete Algorithms (SODA). ACM-SIAM, January 2002.
Frank Thomson Leighton. Introduction to Parallel Algorithms and Architectures: Arrays-Trees-Hypercubes. Morgan Kaufmann, 1992.
Lata Narayanan and Naomi Nishimura. Interval routing on k-trees. Journal of Algorithms, 26(2):325–369, February 1998.
David Peleg. Distributed Computing: A Locality-Sensitive Approach. SIAM Monographs on Discrete Mathematics and Applications, 2000.
Erich Prisner. Distance approximating spanning trees. In 14th Annual Symposium on Theoretical Aspects of Computer Science (STACS), volume 1200 of Lecture Notes in Computer Science, pages 499–510. Springer, 1997.
David Peleg and Alejandro A. Schäffer. Graph spanners.Journal of Graph Theory, 13(1):99–116, 1989.
David Peleg and Eli Upfal. A trade-off between space and efficiency for routing tables. Journal of the ACM, 36(3):510–530, July 1989.
Neil Robertson and Paul D. Seymour. Graph minors. II. Algorithmic aspects of tree-width. Journal of Algorithms, 7:309–322, 1986.
Nicola Santoro and Ramez Khatib. Labelling and implicit routing in networks. The Computer Journal, 28(1):5–8, February 1985.
Mikkel Thorup. Compact oracles for reachability and approximate distances in planar digraphs. In 42th Annual IEEE Symposium on Foundations of Computer Science (FOCS). IEEE Computer Society Press, October 2001.
Mikkel Thorup and Uri Zwick. Compact routing schemes. In 13th Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA), pages 1–10, Hersonissos, Crete, Greece, July 2001. ACM PRESS.
Jan van Leeuwen and Richard B. Tan. Interval routing. The Computer Journal, 30(4):298–307, 1987.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dourisboure, Y. (2002). An Additive Stretched Routing Scheme for Chordal Graphs. In: Goos, G., Hartmanis, J., van Leeuwen, J., Kučera, L. (eds) Graph-Theoretic Concepts in Computer Science. WG 2002. Lecture Notes in Computer Science, vol 2573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36379-3_14
Download citation
DOI: https://doi.org/10.1007/3-540-36379-3_14
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-00331-1
Online ISBN: 978-3-540-36379-8
eBook Packages: Springer Book Archive