A Survey of Algorithms and Models for List Update

Abstract

The list update problem was first studied by McCabe [47] more than 45 years ago under distributional analysis in the context of maintaining a sequential file. In 1985, Sleator and Tarjan [55] introduced the competitive ratio framework for the study of worst case behavior on list update algorithms. Since then, many deterministic and randomized online algorithms have been proposed and studied under this framework. The standard model as originally introduced has a peculiar cost function for the rearrangement of the list after each search operation. To address this, several variants have been introduced, chiefly the MRM model (Martinez and Roura, [46]; Munro, [49]), the paid exchange model, and the compression model. Additionally, the list update problem has been studied under locality of reference assumptions, and several models have been proposed to capture locality of input sequences. This survey gives a brief overview of the main list update algorithms, the main alternative cost models, and the related results for list update with locality of reference. Open problems and directions for future work are included.