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

Abstract

The k-server problem is one of the most fundamental on- line problems. The problem is to schedule k mobile servers to serve a sequence of service points in a metric space to mimize the total mileage. The k-server conjecture [11] that states that there exists an optimal k- competitive on-line algorithm has been open for over 10 years. The top candidate on-line algorithm for settling this conjecture is the Work Function Algorithm (WFA) which was recently shown [7,9] 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.