Skip to main content

Improved Compact Routing Scheme for Chordal Graphs

  • Conference paper
  • First Online:
Distributed Computing (DISC 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2508))

Included in the following conference series:

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, a routing scheme using routing tables and addresses of O(log3 n/ log log n) bits per node, and O(log2 n/log log n) bit not alterable headers 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 a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Baruch Awerbuch, Amotz Bar-Noy, Nathan Linial, and David Peleg. Compact distributed data structures for adaptive routing. In 21st Symposium on Theory of Computing (STOC), volume 2, pages 230–240, May 1989.

    Google Scholar 

  2. Baruch Awerbuch, Amotz Bar-Noy, Nathan Linial, and David Peleg. Improved routing strategies with succinct tables. Journal of Algorithms, 11(3):307–341, September 1990.

    Google Scholar 

  3. Baruch Awerbuch and David Peleg. Sparse partitions. In 31th Symposium on Foundations of Computer Science (FOCS), pages 503–513. IEEE Computer Society Press, 1990.

    Google Scholar 

  4. Baruch Awerbuch and David Peleg. Routing with polynomial communication-space trade-off. SIAM Journal on Discrete Mathematics, 5(2):151–162, May 1992.

    Google Scholar 

  5. 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 

  6. 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 

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

    Google Scholar 

  8. Yon Dourisboure. An additive stretched routing scheme for chordal graphs. In 28-th International Workshop on Graph-Theoretic Concepts in Computer Science (WG’ 02), June 2002. To appear.

    Google Scholar 

  9. Pierre Fraigniaud and Cyril Gavoille. Universal routing schemes. Journal of Distributed Computing, 10:65–78, 1997.

    Article  Google Scholar 

  10. Pierre Fraigniaud and Cyril Gavoille. Routing in trees. In Fernando Orejas, Paul G. Spirakis, and Jan van Leeuwen, editors, 28th International Colloquium on Automata, Languages and Programming (ICALP), volume 2076 of Lecture Notes in Computer Science, pages 757–772. Springer, July 2001.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  14. Cyril Gavoille and Marc Gengler. Space-efficiency of routing schemes of stretch factor three. Journal of Parallel and Distributed Computing, 61:679–687, 2001.

    Article  MATH  Google Scholar 

  15. Cyril Gavoille and Nicolas Hanusse. Compact routing tables for graphs of bounded genus. In Jiří Wiedermann, Peter van Emde Boas, and Mogens Nielsen, editors, 26 th 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 

  16. Cyril Gavoille, Michal Katz, Nir A. Katz, Christophe Paul, and David Peleg. Approximate distance labeling schemes. Research Report RR-1250-00, LaBRI, University of Bordeaux, 351, cours de la Libération, 33405 Talence Cedex, France, December 2000.

    Google Scholar 

  17. Cyril Gavoille and Stéphane Pérennès. Memory requirement for routing in distributed networks. In 15 th Annual ACM Symposium on Principles of Distributed Computing (PODC), pages 125–133. ACM PRESS, May 1996.

    Google Scholar 

  18. Haim Kaplan and Tova Milo. Short and simple labels for small distances and other functions. In 7 th International Workshop on Algorithms and Data Structures (WADS), volume 2125 of Lecture Notes in Computer Science, pages 32–40. Springer, August 2001.

    Chapter  Google Scholar 

  19. 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 

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

    Google Scholar 

  21. Hsueh-I Lu. Improved comact routing tabels for planar networks via orderly spanning trees. In 8 th Annual International Computing & Combinatorics Conference (COCOON), volume Lectures Notes in Computer Science. Springer, August 2002.

    Google Scholar 

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

    Google Scholar 

  23. David Peleg. Distributed Computing: A Locality-S ensitive Approach. SIAM Monographs on Discrete Mathematics and Applications, 2000.

    Google Scholar 

  24. David Peleg. Informative labeling schemes for graphs. In 25th International Symposium on Mathematical Foundations of Computer Science (MFCS), volume 1893 of Lecture Notes in Computer Science, pages 579–588. Springer, August 2000.

    Google Scholar 

  25. Erich Prisner. Distance approximating spanning trees. In 14 th Annual Symposium on Theoretical Aspects of Computer Science (STACS), volume 1200 of Lecture Notes in Computer Science, pages 499–510. Springer, 1997.

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  27. 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.

    Google Scholar 

  28. 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 

  29. Mikkel Thorup. Compact oracles for reachability and approximate distances in planar digraphs. In 42 th Annual IEEE Symposium on Foundations of Computer Science (FOCS). IEEE Computer Society Press, October 2001.

    Google Scholar 

  30. Mikkel Thorup and Uri Zwick. Approximate distance oracles. In 33rd Annual ACM Symposium on Theory of Computing (STOC), pages 183–192, Hersonissos, Crete, Greece, July 2001.

    Google Scholar 

  31. Mikkel Thorup and Uri Zwick. Compact routing schemes. In 13 th Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA), pages 1–10, Hersonissos, Crete, Greece, July 2001. ACM PRESS.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Dourisboure, Y., Gavoille, C. (2002). Improved Compact Routing Scheme for Chordal Graphs. In: Malkhi, D. (eds) Distributed Computing. DISC 2002. Lecture Notes in Computer Science, vol 2508. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36108-1_17

Download citation

  • DOI: https://doi.org/10.1007/3-540-36108-1_17

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00073-0

  • Online ISBN: 978-3-540-36108-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics