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Tight Bounds for Double Coverage Against Weak Adversaries

  • Nikhil Bansal
  • Marek Eliáš
  • Łukasz Jeż
  • Grigorios Koumoutsos
  • Kirk Pruhs
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9499)

Abstract

We study the Double Coverage (DC) algorithm for the k-server problem in the (hk)-setting, i.e. when DC with k servers is compared against an offline optimum algorithm with \(h \le k\) servers. It is well-known that DC is k-competitive for \(h=k\). We prove that even if \(k>h\) the competitive ratio of DC does not improve; in fact, it increases up to \(h+1\) as k grows. In particular, we show matching upper and lower bounds of \(\frac{k(h+1)}{k+1}\) on the competitive ratio of DC on any tree metric.

Keywords

Competitive Ratio Double Coverage Online Algorithm Deterministic Algorithm Request Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Bartal, Y., Koutsoupias, E.: On the competitive ratio of the work function algorithm for the k-server problem. Theor. Comput. Sci. 324(2–3), 337–345 (2004)MATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press, Cambridge (1998)MATHGoogle Scholar
  3. 3.
    Chrobak, M., Karloff, H.J., Payne, T.H., Vishwanathan, S.: New results on server problems. SIAM J. Discrete Math. 4(2), 172–181 (1991)MATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Chrobak, M., Larmore, L.L.: An optimal on-line algorithm for k-servers on trees. SIAM J. Comput. 20(1), 144–148 (1991)MATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    Koutsoupias, E.: Weak adversaries for the k-server problem. In: Proceedings of the 40th Symposium on Foundations of Computer Science (FOCS), pp. 444–449 (1999)Google Scholar
  6. 6.
    Koutsoupias, E., Papadimitriou, C.H.: On the k-server conjecture. J. ACM 42(5), 971–983 (1995)MATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    Manasse, M.S., McGeoch, L.A., Sleator, D.D.: Competitive algorithms for server problems. J. ACM 11(2), 208–230 (1990)MATHMathSciNetGoogle Scholar
  8. 8.
    Sleator, D.D., Tarjan, R.E.: Amortized efficiency of list update and paging rules. Commun. ACM 28(2), 202–208 (1985)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Young, N.E.: The k-server dual and loose competitiveness for paging. Algorithmica 11(6), 525–541 (1994)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Nikhil Bansal
    • 1
  • Marek Eliáš
    • 1
  • Łukasz Jeż
    • 1
    • 2
  • Grigorios Koumoutsos
    • 1
  • Kirk Pruhs
    • 3
  1. 1.Eindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.Institute of Computer ScienceUniversity of WrocławWrocławPoland
  3. 3.University of PittsburghPittsburghUSA

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