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International Workshop on Graph-Theoretic Concepts in Computer Science

WG 2002: Graph-Theoretic Concepts in Computer Science pp 150–163Cite as

An Additive Stretched Routing Scheme for Chordal Graphs

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2573))

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.

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References

  1. Stephen Alstrup and Theis Rauhe. Improved labeling scheme for ancestor queries. In 13th Symposium on Discrete Algorithms (SODA). ACM-SIAM, January 2001. To appear.

    Google Scholar 

  2. Andreas Brandstädt, Victor Chepoi, and Feodor Dragan. Distance approximating trees for chordal and dually chordal graphs. Journal of Algorithms, 30:166–184, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  3. Andreas Brandstädt, Van Bang Le, and Jeremy P. Spinrad. Graph Classes-A survey. SIAM Monographs on Discrete Mathematics and Applications, Philadelphia, 1999.

    Google Scholar 

  4. Reinhard Diestel. Graph Theory (second edition), volume 173 of Graduate Texts in Mathematics. Springer, February 2000.

    Google Scholar 

  5. 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.

    Google Scholar 

  6. 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.

    Google Scholar 

  7. Greg N. Frederickson and Ravi Janardan. Efficient message routing in planar networks. SIAM Journal on Computing, 18(4):843–857, August 1989.

    Article  MATH  MathSciNet  Google Scholar 

  8. Greg N. Frederickson and Ravi Janardan. Space-efficient message routing in c-decomposable networks. SIAM Journal on Computing, 19(1):164–181, February 1990.

    Article  MATH  MathSciNet  Google Scholar 

  9. Cyril Gavoille. A survey on interval routing. Theoretical Computer Science, 245(2):217–253, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  10. Cyril Gavoille. Routing in distributed networks: Overview and open problems. ACM SIGACT News-Distributed Computing Column, 32(1), March 2001. To appear.

    Google Scholar 

  11. Cyril Gavoille. Space lower bounds for routing in chordal graphs with additive stretch, 2002. In preparation.

    Google Scholar 

  12. 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.

    Chapter  Google Scholar 

  13. 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.

    Google Scholar 

  14. 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.

    Google Scholar 

  15. 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.

    Google Scholar 

  16. Frank Thomson Leighton. Introduction to Parallel Algorithms and Architectures: Arrays-Trees-Hypercubes. Morgan Kaufmann, 1992.

    Google Scholar 

  17. Lata Narayanan and Naomi Nishimura. Interval routing on k-trees. Journal of Algorithms, 26(2):325–369, February 1998.

    Article  MATH  MathSciNet  Google Scholar 

  18. David Peleg. Distributed Computing: A Locality-Sensitive Approach. SIAM Monographs on Discrete Mathematics and Applications, 2000.

    Google Scholar 

  19. 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.

    Google Scholar 

  20. David Peleg and Alejandro A. Schäffer. Graph spanners.Journal of Graph Theory, 13(1):99–116, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  21. 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.

    Article  MATH  MathSciNet  Google Scholar 

  22. Neil Robertson and Paul D. Seymour. Graph minors. II. Algorithmic aspects of tree-width. Journal of Algorithms, 7:309–322, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  23. Nicola Santoro and Ramez Khatib. Labelling and implicit routing in networks. The Computer Journal, 28(1):5–8, February 1985.

    Article  MATH  MathSciNet  Google Scholar 

  24. 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.

    Google Scholar 

  25. 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.

    Google Scholar 

  26. Jan van Leeuwen and Richard B. Tan. Interval routing. The Computer Journal, 30(4):298–307, 1987.

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. LaBRI, Université Bordeaux, Bordeaux

    Yon Dourisboure

Authors
  1. Yon Dourisboure
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Editor information

Editors and Affiliations

  1. Karlsruhe University, Germany

    Gerhard Goos

  2. Cornell University, NY, USA

    Juris Hartmanis

  3. Utrecht University, The Netherlands

    Jan van Leeuwen

  4. Department of Applied Mathematics, Charles University, Malostranské nám. 25, 118 00, Prague, Czech Republic

    Luděk Kučera

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© 2002 Springer-Verlag Berlin Heidelberg

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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

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  • DOI: https://doi.org/10.1007/3-540-36379-3_14

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00331-1

  • Online ISBN: 978-3-540-36379-8

  • eBook Packages: Springer Book Archive

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