Algorithmica

, Volume 36, Issue 3, pp 249–260 | Cite as

Static Optimality and Dynamic Search-Optimality in Lists and Trees

  • Blum
  • Chawla
  • Kalai
Article

Abstract

Adaptive data structures form a central topic of on-line algorithms research. The area of Competitive Analysis began with the results of Sleator and Tarjan showing that splay trees achieve static optimality for search trees, and that Move-to-Front is constant competitive for the list update problem [ST1], [ST2]. In a parallel development, powerful algorithms have been developed in Machine Learning for problems of on-line prediction [LW], [FS]. This paper is inspired by the observation made in [BB] that if computational decision-making costs are not considered, then these ``weighted experts'' techniques from Machine Learning allow one to achieve a 1+ε ratio against the best static object in hindsight for a wide range of data structure problems.

In this paper we give two results. First, we show that for the case of lists , we can achieve a 1+ε ratio with respect to the best static list in hindsight, by a simple efficient algorithm. This algorithm can then be combined with existing results to achieve good static and dynamic bounds simultaneously. Second, for trees, we show a (computationally in efficient) algorithm that achieves what we call ``dynamic search optimality'': dynamic optimality if we allow the on-line algorithm to make free rotations after each request. We hope this to be a step towards solving the longstanding open problem of achieving true dynamic optimality for trees.

Keywords

Adaptive data structures Binary search trees Competitive Analysis Experts Analysis 

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Copyright information

© Springer-Verlag New York Inc. 2003

Authors and Affiliations

  • Blum
    • 1
  • Chawla
    • 1
  • Kalai
    • 2
  1. 1.Computer Science Department, Carnegie Mellon University, Pittsburgh, PA 15213, USA. avrim@cs.cmu.edu, shuchi@cs.cmu.edu.US
  2. 2.Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA. akalai@math.mit.edu.US

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