Work function algorithm can forget history without losing competitiveness

TL;DR

This paper introduces a condition under which the Work Function Algorithm can discard its entire request history without sacrificing its competitive performance, enabling constant-time request processing in practical metric spaces.

Contribution

It provides a theoretical condition allowing WFA to forget history without losing competitiveness, improving efficiency for long request sequences.

Findings

WFA can restart from scratch without losing competitiveness under certain conditions.

In practical metric spaces, the history length before restart is bounded by a constant.

This results in O(1) time complexity per request in typical scenarios.

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.