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A Tight Bound on the Number of Mobile Servers to Guarantee the Mutual Transferability Among Dominating Configurations

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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

In this paper, we propose a new framework to provide continuous services to users by a collection of mobile servers distributed over an interconnection network. We model those mobile servers as a subset of host computers, and assume that a user host can receive the service if at least one adjacent host computer (including itself) plays the role of a server; i.e., we assume that the service could not be routed via the interconnection network. The main results obtained in this paper are summarized as follows: For the class of trees with n hosts, ⌈(n+1)/2⌉ mobile servers are necessary and sufficient to realize continuous services by the mobile servers, and for the class of Hamiltonian graphs with n hosts, ⌈(n+1)/3⌉ mobile servers are necessary and sufficient.

This research was partially supported by the Grant-in-Aid for Scientific Research.

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References

  1. Atallah, M.J., Manacher, G.K., Urrutia, J.: Finding a minimum independent dominating set in a permutation graph. Discrete Appl. Math. 21, 177–183 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bange, D.W., Barkauskas, A.E., Slater, P.T.: Efficient dominating sets in graphs. In: Ringeisen, R.D., Roberts, F.S. (eds.) Applications of Discrete Mathematics, pp. 189–199. SIAM, Philadelphia (1988)

    Google Scholar 

  3. Bertossi, A.A.: On the domatic number of interval graphs. Information Processing Letters 28(6), 275–280 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  4. Chang, G.J., Rangan, C.P., Coorg, S.R.: Weighted independent perfect domination on cocomparability graphs. Technical Report 93-24, DIMACS (April 1993)

    Google Scholar 

  5. Cockayne, E.J., Hedetniemi, S.T.: Optimal domination in graphs. IEEE Trans. Circuit and Systems CAS-22, 855–857 (1975)

    Article  MathSciNet  Google Scholar 

  6. Cockayne, E.J., Hedetniemi, S.T.: Towards a theory of domination in graphs. Networks 7, 247–261 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  7. Dai, F., Wu, J.: An Extended Localized Algorithm for Connected Dominating Set Formation in Ad Hoc Wireless Networks. IEEE Transactions on Parallel and Distributed Systems 53(10), 1343–1354 (2004)

    Google Scholar 

  8. Fujita, S., Yamashita, M., Kameda, T.: A Study on r-Configurations – A Resource Assignment Problem on Graphs. SIAM J. Discrete Math. 13(2), 227–254 (2000)

    Article  MathSciNet  Google Scholar 

  9. Fujita, S., Liang, Y.: How to Provide Continuous Services by Mobile Servers in Communication Networks. In: Liew, K.-M., Shen, H., See, S., Cai, W. (eds.) PDCAT 2004. LNCS, vol. 3320, pp. 337–340. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  10. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman and Company, San Francisco (1979)

    MATH  Google Scholar 

  11. Guha, S., Khuller, S.: Approximation Algorithms for Connected Dominating Sets. In: Díaz, J. (ed.) ESA 1996. LNCS, vol. 1136, pp. 179–193. Springer, Heidelberg (1996)

    Google Scholar 

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

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  14. Irving, R.W.: On approximating the minimum independent dominating set. Information Processing Letters 37, 197–200 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  15. Livingston, M., Stout, Q.F.: Perfect dominating sets. Congressus Numerantium 79, 187–203 (1990)

    MATH  MathSciNet  Google Scholar 

  16. Lu, T.L., Ho, P.H., Chang, G.J.: The domatic number problem in interval graphs. SIAM J. Disc. Math. 3, 531–536 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  17. Matheson, L.R., Tarjan, R.E.: Dominating sets in planar graphs. Technical Report TR-461-94, Dept. of Computer Science, Princeton University (May 1994)

    Google Scholar 

  18. Srinivasa Rao, A., Rangan, C.P.: Linear algorithm for domatic number problem on interval graphs. Information Processing Letters 33(1), 29–33 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  19. Wu, J., Li, H.: Domination and Its Applications in Ad Hoc Wireless Networks with Unidirectional Links. In: Proc. of International Conference on Parallel Processing, pp. 189–200 (2000)

    Google Scholar 

  20. Wu, J.: Extended Dominating-Set-Based Routing in Ad Hoc Wireless Networks with Unidirectional Links. IEEE Transactions on Parallel and Distributed Computing 22, 327–340 (2002)

    Google Scholar 

  21. Yen, C.C., Lee, R.C.T.: The weighted perfect domination problem. Information Processing Letters 35, 295–299 (1990)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Information Engineering, Graduate School of Engineering, Hiroshima University,  

    Satoshi Fujita

Authors
  1. Satoshi Fujita
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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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© 2005 Springer-Verlag Berlin Heidelberg

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Fujita, S. (2005). A Tight Bound on the Number of Mobile Servers to Guarantee the Mutual Transferability Among Dominating Configurations. 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_57

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  • DOI: https://doi.org/10.1007/11602613_57

  • 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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