Work function algorithm can forget history without losing competitiveness

Abstract

The Work Function Algorithm is the most effective deterministic on-line algorithm for the k-server problem. Koutsoupias and Papadimitriou proved WFA is (2k-1) competitive. However the best known implementation of WFA requires time O(i^2) to process request r_i and this makes WFA impractical for long sequences of requests. The O(i^2) time is spent to compute the work function on the whole history of past requests. In order to make constant the time to process a request, Rudec and Menger proposed to restrict the history to a moving window of fixed size. However WFA restricted to a moving window loses its competitiveness. Here we give a condition that allows WFA to forget the whole previous history and restart from scratch without losing competitiveness. Moreover for most of the metric spaces of practical interest (finite or bounded spaces) there is a constant bound on the length of the history before the condition is verified and this makes O(1) the time to process each request.