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Dominating Sets in Web Graphs

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Algorithms and Models for the Web-Graph (WAW 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3243))

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Abstract

In this paper we study the size of generalised dominating sets in two graph processes which are widely used to model aspects of the world-wide web. On the one hand, we show that graphs generated this way have fairly large dominating sets (i.e. linear in the size of the graph). On the other hand, we present efficient strategies to construct small dominating sets.

The algorithmic results represent an application of a particular analysis technique which can be used to characterise the asymptotic behaviour of a number of dynamic processes related to the web.

The first two authors were partially supported by a Royal Society Grant under the European Science Exchange Programme.

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References

  1. Alon, N., Spencer, J.H., Erdős, P.: The Probabilistic Method. John Wiley & Sons, Chichester (1992)

    Google Scholar 

  2. Alzoubi, K., Wan, P.J., Frieder, O.: Message-optimal connected dominating sets in mobile ad hoc networks. In: Proc. 3rd ACM Internat. Symp. on Mobile Ad-hoc Networking & Computing, pp. 157–164 (2002)

    Google Scholar 

  3. Barabási, A., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bender, E.A., Canfield, E.R.: The asymptotic number of labeled graphs with given degree sequences. JCT A 24, 296–307 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bollobás, B., Riordan, O., Spencer, J., Tusnády, G.: The degree sequence of a scale-free random graph process. RSA 18, 279–290 (2001)

    MathSciNet  MATH  Google Scholar 

  6. Broder, A., Kumar, R., Maghoul, F., Raghavan, P., Rajagopalan, S., Stata, R., Tomkins, A., Wiener, J.: Graph structure in the web. In: Proc. 9th WWW, pp. 309–320 (2000)

    Google Scholar 

  7. Cockayne, E., Goodman, S., Hedetniemi, S.: A linear algorithm for the domination number of a tree. IPL 4, 41–44 (1975)

    Article  MATH  Google Scholar 

  8. Cooper, C.: The age specific degree distribution of web-graphs. Combinatorics Probability and Computing (Submitted) (2002)

    Google Scholar 

  9. Cooper, C., Frieze, A.: A general model of web graphs. RSA 22, 311–335 (2003)

    MathSciNet  MATH  Google Scholar 

  10. Duckworth, W., Zito, M.: Sparse hypercube 3-spanners. DAM 103, 289–295 (2000)

    MathSciNet  MATH  Google Scholar 

  11. Eidenbenz, S.: Online dominating set and variations on restricted graph classes. Technical Report 380, Department of Computer Science, ETH Zürich (2002)

    Google Scholar 

  12. Feige, U.: A threshold of ln n for approximating set cover. J.ACM 45, 634–652 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  13. Garey, M.R., Johnson, D.S.: Strong NP-Completeness results: Motivation, examples, and implications. Journal of the Association for Computing Machinery 25(3), 499–508 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  14. Harary, F., Haynes, T.W.: Double domination in graphs. Ars Comb. 55, 201–213 (2000)

    MathSciNet  MATH  Google Scholar 

  15. Haynes, T.W., Hedetniemi, S.T., Slater, P.J.: Domination in Graphs: Advanced Topics. Marcel Dekker, New York (1998)

    MATH  Google Scholar 

  16. Haynes, T.W., Hedetniemi, S.T., Slater, P.J.: Fundamentals of Domination in Graphs. Marcel Dekker, New York (1998)

    MATH  Google Scholar 

  17. King, G.-H., Tzeng, W.-G.: On-line algorithms for the dominating set problem. IPL 61, 11–14 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  18. Klasing, R., Laforest, C.: Hardness results and approximation algorithms of k-tuple domination in graphs. IPL 89, 75–83 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  19. Kumar, R., Raghavan, P., Rajagopalan, S., Sivakumar, D., Tomkins, A., Upfal, E.: The web as a graph. In: Proc. ACM Symp. on PODS, pp. 1–10 (2000)

    Google Scholar 

  20. Levene, M., Wheeldon, R.: Web dynamics. Software Focus 2, 31–38 (2001)

    Article  Google Scholar 

  21. Liao, C.-S., Chang, G.J.: k-tuple domination in graphs. IPL 87, 45–50 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  22. Stojmenovic, I., Seddigh, M., Zunic, J.: Dominating sets and neighbor elimination-based broadcasting algorithms in wireless networks. IEEE Trans. Parallel and Dist. Systems 13, 14–25 (2002)

    Article  Google Scholar 

  23. Watts, D.J., Strogatz, S.H.: Collective dynamics of ’small-world’ networks. Nature 393(4), 440–442 (1998)

    Article  Google Scholar 

  24. Wieland, B., Godbole, A.P.: On the domination number of a random graph. Elec. J. Combinat. 8:# R37 (2001)

    Google Scholar 

  25. Wormald, N.C.: The differential equation method for random graph processes and greedy algorithms. In: Karoński, M., Prömel, H.J. (eds.) Lectures on Approximation and Randomized Algorithms, pp. 73–155, PWN, Warsaw (1999)

    Google Scholar 

  26. Zito, M.: Greedy algorithms for minimisation problems in random regular graphs. In: Meyer auf der Heide, F. (ed.) ESA 2001. LNCS, vol. 2161, pp. 524–536. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, King’s College, London, WC2R 2LS, UK

    Colin Cooper

  2. MASCOTTE project, I3S-CNRS/INRIA, Université de Nice-Sophia Antipolis, 2004 Route des Lucioles, BP 93, F-06902 Cedex, Sophia Antipolis, France

    Ralf Klasing

  3. Department of Computer Science, University of Liverpool, Peach Street, Liverpool, L69 7ZF, UK

    Michele Zito

Authors
  1. Colin Cooper
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  2. Ralf Klasing
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  3. Michele Zito
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Editor information

Editors and Affiliations

  1. University of Rome “La Sapienza”, Rome, Italy

    Stefano Leonardi

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© 2004 Springer-Verlag Berlin Heidelberg

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Cooper, C., Klasing, R., Zito, M. (2004). Dominating Sets in Web Graphs. In: Leonardi, S. (eds) Algorithms and Models for the Web-Graph. WAW 2004. Lecture Notes in Computer Science, vol 3243. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30216-2_3

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  • DOI: https://doi.org/10.1007/978-3-540-30216-2_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23427-2

  • Online ISBN: 978-3-540-30216-2

  • eBook Packages: Springer Book Archive

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