Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

General Compact Labeling Schemes for Dynamic Trees

  • Conference paper
Distributed Computing (DISC 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3724))

Included in the following conference series:

  • 654 Accesses

Abstract

An F- labeling scheme is composed of a marker algorithm for labeling the vertices of a graph with short labels, coupled with a decoder algorithm allowing one to compute F(u,v) of any two vertices u and v directly from their labels. As applications for labeling schemes concern mainly large and dynamically changing networks, it is of interest to study distributed dynamic labeling schemes.

A general method for constructing labeling schemes for dynamic trees was previously developed in [28]. This method is based on extending an existing static tree labeling scheme to the dynamic setting. This approach fits many natural functions on trees, such as distance, routing, nearest common ancestor etc.. The resulted dynamic schemes incur overheads (over the static scheme) on the label size and on the communication complexity. In particular, all their schemes yield a multiplicative overhead factor of Ω(log n) on the label sizes of the static schemes. Following [28], we develop a different general method for extending static labeling schemes to the dynamic tree settings. Our method fits the same class of tree functions. In contrast to the above paper, our trade-off is designed to minimize the label size on expense of communication.

Informally, for any k we present a dynamic labeling scheme incurring multiplicative overhead factors (over the static scheme) of O(log k n) on the label size and O(klog k n) on the amortized message complexity. In particular, by setting \(k = \sqrt{n}\), we obtain dynamic labeling schemes with asymptotically optimal label sizes and sublinear amortized message complexity for the routing and the nearest common ancestor functions.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Afek, Y., Awerbuch, B., Plotkin, S.A., Saks, M.: Local management of a global resource in a communication. J. of the ACM 43, 1–19 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  2. Alstrup, S., Bille, P., Rauhe, T.: Labeling schemes for small distances in trees. In: Proc. 14th ACM-SIAM Symp. on Discrete Algorithms (January 2003)

    Google Scholar 

  3. Alstrup, S., Gavoille, C., Kaplan, H., Rauhe, T.: Nearest Common Ancestors: A Survey and a new Distributed Algorithm. Theory of Computing Systems 37, 441–456 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  4. Alstrup, S., Holm, J., Thorup, M.: Maintaining Center and Median in Dynamic Trees. In: Halldórsson, M.M. (ed.) SWAT 2000. LNCS, vol. 1851, p. 46. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  5. Abiteboul, S., Kaplan, H., Milo, T.: Compact labeling schemes for ancestor queries. In: Proc. 12th ACM-SIAM Symp. on Discrete Algorithms (January 2001)

    Google Scholar 

  6. Alstrup, S., Rauhe, T.: Improved Labeling Scheme for Ancestor Queries. In: Proc. 19th ACM-SIAM Symp. on Discrete Algorithms (January 2002)

    Google Scholar 

  7. Breuer, M.A., Folkman, J.: An unexpected result on coding the vertices of a graph. J. of Mathematical Analysis and Applications 20, 583–600 (1967)

    Article  MATH  MathSciNet  Google Scholar 

  8. Breuer, M.A.: Coding the vertexes of a graph. IEEE Trans. on Information Theory IT-12, 148–153 (1966)

    Article  MATH  MathSciNet  Google Scholar 

  9. Cole, R., Hariharan, R.: Dynamic LCA Queries on Trees. In: Proc. 10th ACM-SIAM Symp. on Discrete Algorithms, pp. 235–244 (1999)

    Google Scholar 

  10. Cohen, E., Halperin, E., Kaplan, H., Zwick, U.: Reachability and Distance Queries via 2-hop Labels. In: Proc. 13th ACM-SIAM Symp. on Discrete Algorithms (January 2002)

    Google Scholar 

  11. Cohen, E., Kaplan, H., Milo, T.: Labeling dynamic XML trees. In: Proc. 21st ACM Symp. on Principles of Database Systems (June 2002)

    Google Scholar 

  12. Eppstein, D., Galil, Z., Italiano, G.F.: Dynamic Graph Algorithms. In: Atallah, M.J. (ed.) Algorithms and Theoretical Computing Handbook, ch. 8. CRC Press, Boca Raton (1999)

    Google Scholar 

  13. Fraigniaud, P., Gavoille, C.: Routing in trees. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds.) ICALP 2001. LNCS, vol. 2076, pp. 757–772. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  14. Fraigniaud, P., Gavoille, C.: A space lower bound for routing in trees. In: Proc. 19th Symp. on Theoretical Aspects of Computer Science (March 2002)

    Google Scholar 

  15. Feigenbaum, J., Kannan, S.: Dynamic Graph Algorithms. In: Handbook of Discrete and Combinatorial Mathematics. CRC Press, Boca Raton (2000)

    Google Scholar 

  16. Gavoille, C., Paul, C.: Split decomposition and distance labelling: an optimal scheme for distance hereditary graphs. In: Proc. European Conf. on Combinatorics, Graph Theory and Applications (September 2001)

    Google Scholar 

  17. Gavoille, C., Peleg, D.: Compact and Localized Distributed Data Structures. J. of Distributed Computing 16, 111–120 (2003)

    Article  Google Scholar 

  18. Gavoille, C., Katz, M., Katz, N.A., Paul, C., Peleg, D.: Approximate Distance Labeling Schemes. In: Meyer auf der Heide, F. (ed.) ESA 2001. LNCS, vol. 2161, pp. 476–488. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  19. Gavoille, C., Peleg, D., Pérennes, S., Raz, R.: Distance labeling in graphs. In: Proc. 12th ACM-SIAM Symp. on Discrete Algorithms, January 2001, pp. 210–219 (2001)

    Google Scholar 

  20. Holm, J., Lichtenberg, K., Thorup, M.: Poly-logarithmic deterministic fully-dynamic algorithms for connectivity, minimum spanning tree, 2-edge, and biconnectivity. J. of the ACM 48(4), 723–760 (2001)

    Article  MATH  Google Scholar 

  21. Kannan, S., Naor, M., Rudich, S.: Implicit representation of graphs. In: Proc. 20th ACM Symp. on Theory of Computing, May 1988, pp. 334–343 (1988)

    Google Scholar 

  22. Kaplan, H., Milo, T.: Short and simple labels for small distances and other functions. In: Dehne, F., Sack, J.-R., Tamassia, R. (eds.) WADS 2001. LNCS, vol. 2125, p. 246. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  23. Kaplan, H., Milo, T.: Parent and ancestor queries using a compact index. In: Proc. 20th ACM Symp. on Principles of Database Systems (May 2001)

    Google Scholar 

  24. Kaplan, H., Milo, T., Shabo, R.: A Comparison of Labeling Schemes for Ancestor Queries. In: Proc. 19th ACM-SIAM Symp. on Discrete Algorithms (January 2002)

    Google Scholar 

  25. Katz, M., Katz, N.A., Korman, A., Peleg, D.: Labeling schemes for flow and connectivity. In: Proc. 19th ACM-SIAM Symp. on Discrete Algorithms (January 2002)

    Google Scholar 

  26. Katz, M., Katz, N.A., Peleg, D.: Distance labeling schemes for well-separated graph classes. In: Proc. 17th Symp. on Theoretical Aspects of Computer Science, February 2000, pp. 516–528 (2000)

    Google Scholar 

  27. Korman, A., Peleg, D.: Labeling Schemes for Weighted Dynamic Trees. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  28. Korman, A., Peleg, D., Rodeh, Y.: Labeling schemes for dynamic tree networks. Theory of Computing Systems 37, 49–75 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  29. Peleg, D.: Proximity-preserving labeling schemes and their applications. In: Widmayer, P., Neyer, G., Eidenbenz, S. (eds.) WG 1999. LNCS, vol. 1665, pp. 30–41. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  30. Peleg, D.: Informative labeling schemes for graphs. In: Nielsen, M., Rovan, B. (eds.) MFCS 2000. LNCS, vol. 1893, pp. 579–588. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  31. Peleg, D.: Distributed Computing: A Locality-Sensitive Approach. SIAM, Philadelphia (2000)

    Book  MATH  Google Scholar 

  32. Sleator, D.D., Tarjan, R.E.: A data structure for dynamic trees. Journal of Computer and System Sciences 26(1), 362–391 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  33. Santoro, N., Khatib, R.: Labelling and implicit routing in networks. The Computer Journal 28, 5–8 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  34. Thorup, M.: Compact oracles for reachability and approximate distances in planar digraphs. J. of the ACM 51, 993–1024 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  35. Thorup, M., Zwick, U.: Compact routing schemes. In: Proc. 13th ACM Symp. on Parallel Algorithms and Architecture, Hersonissos, Crete, Greece, July 2001, pp. 1–10 (2001)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science and Applied Mathematics, The Weizmann Institute of Science, Rehovot, 76100, Israel

    Amos Korman

Authors
  1. Amos Korman
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. CNRS and University Paris Diderot,  

    Pierre Fraigniaud

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Korman, A. (2005). General Compact Labeling Schemes for Dynamic Trees. In: Fraigniaud, P. (eds) Distributed Computing. DISC 2005. Lecture Notes in Computer Science, vol 3724. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11561927_33

Download citation

  • DOI: https://doi.org/10.1007/11561927_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-29163-3

  • Online ISBN: 978-3-540-32075-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation