Two results on the list update problem

Abstract

In this paper we give a randomized on-line algorithm for the list update problem. Sleator and Tarjan show a deterministic algorithm, Move-to-Front, that achieves competitive ratio of ( 2L−1) L for lists of length L. Karp and Raghavan show that no deterministic algorithm can beat 2L (L+1) . We show that Move-to-Front in fact achieves an optimal competitive ratio of 2L (L+1) . We show a randomized algorithm that achieves a competitive ratio of (31L+1) 16(L+1) against an oblivious adversary. This is the first randomized strategy whose competitive factor beats a constant less than 2.