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An Improved Interval Routing Scheme for Almost All Networks Based on Dominating Cliques

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Algorithms and Computation (ISAAC 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3827))

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Abstract

Motivated by the peer-to-peer content sharing systems in large-scale networks, we will study interval routing schemes in Erdös-Rényi random graphs. C. Gavoille and D. Peleg [13] posed an open question of whether almost all networks support a shortest-path interval routing scheme with 1 interval. In this paper, we answer this question partially by proving that in almost all networks, there is an interval routing scheme with 1 interval up to additive stretch 2. Our proof is based on the properties of dominating cliques in random graphs.

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References

  1. Bollobás, B.: Random Graphs, 2nd edn. Cambridge Studies in Advanced Mathmatics 73 (2001)

    Google Scholar 

  2. Bollobás, B., Erdös, P.: Cliques in random graphs. Math. Proc. Cam. Phil. Soc. 80, 419–427 (1976)

    Article  MATH  Google Scholar 

  3. Bononi, L.: A Perspective on P2P Paradigm and Services, Slide courtesy of A. Montresor, http://www.cs.unibo.it/people/faculty/bononi//AdI2004/AdI11.pdf

  4. Buhrman, H., Hoepman, J.-H., Vitányi, P.M.B.: Space-efficient Routing Tables for Almost All Networks and the Incompressibility Method. SIAM Journal on Computing 28(4), 1414–1432 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  5. Buhrman, H., Li, M., Tromp, J., Vitányi, P.M.B.: Kolmogorov Random Graphs and the Incompressibility Method. SIAM Journal on Computing 29(2), 590–599 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  6. Eilam, T., Moran, S., Zaks, S.: The Complexity of the Characterization of Networks Supporting Shortest-Path Interval Routing. In: Krizanc, D., Widmayer, P. (eds.) Proc. 4th Int. Colloquium on Struct. Information & Communication Complexity SIROCCO 1997, pp. 99–111. Carleton Scientific, Ottawa (1997)

    Google Scholar 

  7. Flammini, M., van Leeuwen, J., Marchetti-Spaccamela, A.: The complexity of interval routing on random graphs. The Computer Journal 41(1), 16–25 (1998)

    Article  MATH  Google Scholar 

  8. Fraigniaud, P., Gavoille, C.: Interval Routing Schemes. Algorithmica 21(2), 155–182 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  9. Ganesh, A.J., Kermarrec, A.-M., Massoulié, L.: Peer-to-Peer Membership Management for Gossip-Based Protocols. IEEE Trans. Computers 52(2), 139–149 (2003)

    Article  Google Scholar 

  10. Garey, M.R., Johnson, D.S.: Computers and Intractability. Freeman, New York (1979)

    MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  12. Gavoille, C., Nehéz, M.: Interval routing in reliability networks. Theoretical Computer Science 333(3), 415–432 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  13. Gavoille, C., Peleg, D.: The compactness of interval routing for almost all graphs. SIAM Journal on Computing 31(3), 706–721 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  14. Gavoille, C., Peleg, D., Raspaud, A., Sopena, E.: Small k-Dominating Sets in Planar Graphs with Applications. In: Brandstädt, A., Van Le, B. (eds.) WG 2001. LNCS, vol. 2204, pp. 201–216. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  15. Gross, J.L., Yellen, J.: Handbook of Graph Theory. CRC Press, Boca Raton (2003)

    Book  Google Scholar 

  16. Janson, S., Luczak, T., Rucinski, A.: Random Graphs. John Wiley & Sons, New York (2000)

    MATH  Google Scholar 

  17. Kalbfleisch, J.G.: Complete subgraphs of random hypergraphs and bipartite graphs. In: Proc. 3rd Southeastern Conf. of Combinatorics, Graph Theory and Computing, Florida tlantic University, pp. 297–304 (1972)

    Google Scholar 

  18. Karp, R.M.: Reducibility among combinatorial problems. In: Miller, R.E., Thatcher, J.W. (eds.) Complexity of Computer Computation, pp. 85–103. Plenum Press, New York (1972)

    Google Scholar 

  19. Kermarrec, A.-M., Massoulié, L., Ganesh, A.J.: Probabilistic Reliable Dissemination in Large-Scale Systems. IEEE Trans. Parallel Distrib. Syst. 14(3), 248–258 (2003)

    Article  Google Scholar 

  20. Krioukov, D., Fall, K.R., Yang, X.: Compact Routing on Internet-like Graphs. In: INFOCOM 2004 (2004) (full version published in CoRR cond-mat/0308288, 2003)

    Google Scholar 

  21. Matula, D.W.: The largest clique size in a random graph, Technical report CS 7608, Dept. of Comp. Sci. Southern Methodist University, Dallas (1976)

    Google Scholar 

  22. May, D., Thompson, P.: Transputers and Routers: Components for concurrent machines. INMOS Ltd. (1990)

    Google Scholar 

  23. Nehéz, M.: The compactness lower bound of shortest-path interval routing on n × n tori with random faulty links. Technical Report 582, KAM-DIMATIA Series, Charles University, Praha (2002)

    Google Scholar 

  24. Olejár, D., Toman, E.: On the Order and the Number of Cliques in a Random Graph. Math. Slovaca 47(5), 499–510 (1997)

    MATH  MathSciNet  Google Scholar 

  25. Palmer, E.M.: Graphical Evolution. John Wiley & Sons, Inc., New York (1985)

    MATH  Google Scholar 

  26. Ružička, P.: On efficiency of path systems induced by routing and communication schemes. Computing and Informatics 20(2), 181–205 (2001)

    MATH  MathSciNet  Google Scholar 

  27. van Leeuwen, J., Tan, R.B.: Interval routing. The Computer Journal 30(4), 298–307 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  28. Wieland, B., Godbole, A.P.: On the Domination Number of a Random Graph. Electronic Journal of Combinatorics 8(1), #R37 (2001)

    MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, FEE CTU Prague, Karlovo náměstí 13, 121 35, Praha 2, Czech Republic

    Martin Nehéz

  2. Department of Computer Science, FMPI, Comenius University in Bratislava, Mlynská dolina, 842 48, Bratislava, Slovak Republic

    Daniel Olejár

Authors
  1. Martin Nehéz
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  2. Daniel Olejár
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Editor information

Editors and Affiliations

  1. Department of Computer Science, City University of Hong Kong, Tat Chee Avenue, Kowloon , Hong Kong

    Xiaotie Deng

  2. Department of Computer Science, University of Texas at Dallas, EE/CS Building, 75083, Richardson, TX, USA

    Ding-Zhu Du

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Nehéz, M., Olejár, D. (2005). An Improved Interval Routing Scheme for Almost All Networks Based on Dominating Cliques. In: Deng, X., Du, DZ. (eds) Algorithms and Computation. ISAAC 2005. Lecture Notes in Computer Science, vol 3827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11602613_53

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  • DOI: https://doi.org/10.1007/11602613_53

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-30935-2

  • Online ISBN: 978-3-540-32426-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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