Multi-finger binary search trees
Parinya Chalermsook, Mayank Goswami, L\'aszl\'o Kozma, Kurt Mehlhorn,, and Thatchaphol Saranurak

TL;DR
This paper introduces a new theoretical framework for multi-finger binary search trees, showing they can be efficiently simulated by standard BSTs with only a logarithmic factor overhead, and develops online algorithms that nearly match this bound.
Contribution
It establishes tight bounds for the optimal offline multi-finger BSTs using standard BSTs and introduces new online BST algorithms leveraging $k$-server problem techniques.
Findings
Optimal offline $k$-finger BSTs can be simulated by standard BSTs with $O( ext{log}k)$ overhead.
New online BST algorithms match the offline bounds up to a polylogarithmic factor.
BSTs can efficiently serve queries close to recently accessed items, supporting a form of the unified property.
Abstract
We study multi-finger binary search trees (BSTs), a far-reaching extension of the classical BST model, with connections to the well-studied -server problem. Finger search is a popular technique for speeding up BST operations when a query sequence has locality of reference. BSTs with multiple fingers can exploit more general regularities in the input. In this paper we consider the cost of serving a sequence of queries in an optimal (offline) BST with fingers, a powerful benchmark against which other algorithms can be measured. We show that the -finger optimum can be matched by a standard dynamic BST (having a single root-finger) with an factor overhead. This result is tight for all , improving the factor implicit in earlier work. Furthermore, we describe new online BSTs that match this bound up to a factor. Previously only the…
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Taxonomy
TopicsOptimization and Search Problems · Complexity and Algorithms in Graphs · Auction Theory and Applications
