The generalized two-server problem

We consider the generalized on-line two-server problem in which at each step each server receives a request, which is a point in a metric space. One of the servers has to be moved to its request. Thus, each of the servers is moving in his own metric space. 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 constantcompetitive ratio exists for this problem. We answer this question in the affirmative sense by providing the first constant competitive algorithm for the generalized two-server problem on any metric space. The basic result in this paper 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.

• Type: Journal
• Year: 2006
• Where: JACM
• Authors: René A. Sitters, Leen Stougie
• Keywords: Competitive Algorithm, JACM 2006, Metric Space, Two-server Problem