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A fast work function algorithm for solving the k-server problem

Author

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  • Tomislav Rudec
  • Alfonzo Baumgartner
  • Robert Manger

Abstract

This paper deals with the work function algorithm (WFA) for solving the on-line k-server problem. The paper addresses some practical aspects of the WFA, such as its efficient implementation and its true quality of serving. First, an implementation of the WFA is proposed, which is based on network flows, and which reduces each step of the WFA to only one minimal-cost maximal flow problem instance. Next, it is explained how the proposed implementation can further be simplified if the involved metric space is finite. Also, it is described how actual computing of optimal flows can be speeded up by taking into account special properties of the involved networks. Some experiments based on the proposed implementation and improvements are presented, where actual serving costs of the WFA have been measured on very large problem instances and compared with costs of other algorithms. Finally, suitability of the WFA for solving real-life problems is discussed. Copyright Springer-Verlag 2013

Suggested Citation

  • Tomislav Rudec & Alfonzo Baumgartner & Robert Manger, 2013. "A fast work function algorithm for solving the k-server problem," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(1), pages 187-205, January.
    • Handle: RePEc:spr:cejnor:v:21:y:2013:i:1:p:187-205
    DOI: 10.1007/s10100-011-0222-7
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    Cited by:

    1. Tomislav Rudec & Robert Manger, 2015. "A fast approximate implementation of the work function algorithm for solving the $$k$$ k -server problem," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 23(3), pages 699-722, September.
    2. Bertsimas, Dimitris & Jaillet, Patrick & Korolko, Nikita, 2019. "The K-server problem via a modern optimization lens," European Journal of Operational Research, Elsevier, vol. 276(1), pages 65-78.
    3. Wenming Zhang & Yongxi Cheng, 2020. "A new upper bound on the work function algorithm for the k-server problem," Journal of Combinatorial Optimization, Springer, vol. 39(2), pages 509-518, February.

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