Tight Bounds for Double Coverage Against Weak Adversaries

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


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.


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.


  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)zbMATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press, Cambridge (1998)zbMATHGoogle 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)zbMATHMathSciNetCrossRefGoogle 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)zbMATHMathSciNetCrossRefGoogle 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)zbMATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    Manasse, M.S., McGeoch, L.A., Sleator, D.D.: Competitive algorithms for server problems. J. ACM 11(2), 208–230 (1990)zbMATHMathSciNetGoogle 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
    Email author
  • Kirk Pruhs
    • 3
  1. 1.Eindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.Institute of Computer ScienceUniversity of WrocławWrocławPoland
  3. 3.University of PittsburghPittsburghUSA

Personalised recommendations