Improved space bounds for strongly competitive randomized paging algorithms

Abstract

Paging is a prominent problem in the field of online algorithms. While in the deterministic setting there exist simple and efficient strongly competitive algorithms, in the randomized setting a tradeoff between competitiveness and memory is still not settled. In this paper we address the conjecture in [2], that there exist strongly competitive randomized paging algorithms using o(k) bookmarks, i.e. pages not in cache that the algorithm keeps track of. We prove tighter bounds for Equitable2 [2], showing that it requires less than k bookmarks, more precisely ≈ 0.62 k. We then give a lower bound for Equitable2 showing that it cannot both be strongly competitive and use o(k) bookmarks. Our main result proves the conjecture that there exist strongly competitive paging algorithms using o(k) bookmarks. We propose an algorithm, denoted Partition2, which is a variant of the Partition algorithm in [3]. While Partition is unbounded in its space requirements, Partition2 uses Θ(k/logk) bookmarks. © 2013 Springer-Verlag.