On list update and work function algorithms

Abstract

The list update problem, a well-studied problem in dynamic data structures, can be described abstractly as a metrical task system. In this paper, we prove that a generic metrical task system algorithm, called the work function algorithm, has constant competitive ratio for list update. In the process, we present a new formulation of the well-known “list factoring” technique in terms of a partial order on the elements of the list. This approach leads to a new simple proof that a large class of online algorithms, including Move-To-Front, is (2−1/k)-competitive, for k the list length.