The generalized two-server problem

René A. Sitters*, Leen Stougie

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


We consider the generalized on-line two-server problem in which each server moves in its own metric space. Requests for service arrive one-by-one and every request is represented by two points: one in each metric space. The problem is to move, at every request, one of the two servers to its request-point such that the total distance travelled by the two servers is minimized. The special case in which both metric spaces are the real line is known as the CNN-problem. It has been a well-known open question in on-line optimization if an algorithm with a constant-competitive ratio exists for this problem. We answer this question in the affirmative by providing a constant-competitive algorithm for the generalized two-server problem on any metric space. The basic result in this article is a characterization of competitiveness for metrical service systems that seems much easier to use when looking for a competitive algorithm. The existence of a competitive algorithm for the generalized two-server problem follows rather easily from this result.

Original languageEnglish
Pages (from-to)437-458
Number of pages22
JournalJournal of the Association for Computing Machinery
Issue number3
Publication statusPublished - 2006


  • Competitive analysis
  • k-server problem
  • Metrical service system
  • On-line algorithms
  • Work function


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