On the competitive ratio of the work function algorithm for the k -server problem

Yair Bartal*, Elias Koutsoupias

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

44 Scopus citations


The k-server problem is one of the most fundamental online problems. The problem is to schedule k mobile servers to visit a sequence of points in a metric space with minimum total mileage. The k-server conjecture of Manasse, McGeogh, and Sleator states that there exists a k-competitive online algorithm. The conjecture has been open for over 15 years. The top candidate online algorithm for settling this conjecture is the work function algorithm (WFA) which was shown to have competitive ratio at most 2k-1. In this paper, we lend support to the conjecture that WFA is in fact k-competitive by proving that it achieves this ratio in several special metric spaces: the line, the star, and all metric spaces with k+2 points.

Original languageAmerican English
Pages (from-to)337-345
Number of pages9
JournalTheoretical Computer Science
Issue number2-3 SPEC. ISS.
StatePublished - 20 Sep 2004

Bibliographical note

Funding Information:
∗Corresponding author. E-mail addresses: yair@cs.huji.ac.il (Y. Bartal), elias@di.uoa.gr (E. Koutsoupias). 1Supported in part by a grant of the Israeli Science Foundation (195/02). 2Supported in part by NSF Grant CCR-0105752.


  • Online algorithms
  • The k -server problem
  • Work function


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