Randomized competitive algorithms for the list update problem

We prove upper and lower bounds on the competitiveness of randomized algorithms for the list update problem of Sleator and Tarjan. We give a simple and elegant randomized algorithm that is more competitive than the best previous randomized algorithm due to Irani. Our algorithm uses randomness only during an initialization phase, and from then on runs completely deterministically. It is the first randomized competitive algorithm with this property to beat the deterministic lower bound. We generalize our approach to a model in which access costs are fixed but update costs are scaled by an arbitrary constantd. We prove lower bounds for deterministic list update algorithms and for randomized algorithms against oblivious and adaptive on-line adversaries. In particular, we show that for this problem adaptive on-line and adaptive off-line adversaries are equally powerful.A preliminary version of these results appeared in a joint paper with S. Irani in theProceedings of the 2nd Symposium on Discrete Algorithms, 1991 [17].This research was partially supported by NSF Grants CCR-8808949 and CCR-8958528.This research was partially supported by NSF Grant CCR-9009753.This research was supported in part by the National Science Foundation under Grant CCR-8658139, by DIMACS, a National Science Foundation Science and Technology center, Grant No. NSF-STC88-09648.