Layered Working-Set Trees

TL;DR

This paper introduces layered working-set trees, a binary search tree data structure that guarantees the working-set property in the worst case and approximates the unified bound efficiently, improving theoretical guarantees.

Contribution

It presents the first binary search tree achieving the working-set property in the worst case and approximates the unified bound in the amortized sense.

Findings

Achieves worst-case guarantees for the working-set property.

Approximates the unified bound within a small additive term.

Maintains logarithmic access time close to the working-set bound.

Abstract

The working-set bound [Sleator and Tarjan, J. ACM, 1985] roughly states that searching for an element is fast if the element was accessed recently. Binary search trees, such as splay trees, can achieve this property in the amortized sense, while data structures that are not binary search trees are known to have this property in the worst case. We close this gap and present a binary search tree called a layered working-set tree that guarantees the working-set property in the worst case. The unified bound [Badoiu et al., TCS, 2007] roughly states that searching for an element is fast if it is near (in terms of rank distance) to a recently accessed element. We show how layered working-set trees can be used to achieve the unified bound to within a small additive term in the amortized sense while maintaining in the worst case an access time that is both logarithmic and within a small multiplicative factor of the working-set bound.