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Dynamic optimality and multi-splay trees

Autor: Daniel D Sleator; Chengwen Chris Wang
Editora: Pittsburgh, Pa. : School of Computer Science, Carnegie Mellon University, [2004]
Séries: Research paper (Carnegie Mellon University. School of Computer Science), CMU-CS-04-171.
Edição/Formato   Livro : Inglês
Base de Dados:WorldCat
Resumo:
Abstract: "The Dynamic Optimality Conjecture [ST85] states that splay trees are competitive (with a constant competitive factor) among the class of all binary search tree (BST) algorithms. Despite 20 years of research this conjecture is still unresolved. Recently Demaine et al. [DHIP04] suggested searching for alternative algorithms which have small, but non-constant competitive factors. They proposed tango, a BST  Ler mais...
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Detalhes

Tipo de Material: Recurso Internet
Tipo de Documento: Livro, Recurso Internet
Todos os Autores / Contribuintes: Daniel D Sleator; Chengwen Chris Wang
Número OCLC: 57217789
Notas: "November 5, 2004."
Descrição: 12 p. : ill. ; 28 cm.
Título da Série: Research paper (Carnegie Mellon University. School of Computer Science), CMU-CS-04-171.
Responsabilidade: Daniel Dominic Sleator and Chengwen Chris Wang.

Resumo:

Abstract: "The Dynamic Optimality Conjecture [ST85] states that splay trees are competitive (with a constant competitive factor) among the class of all binary search tree (BST) algorithms. Despite 20 years of research this conjecture is still unresolved. Recently Demaine et al. [DHIP04] suggested searching for alternative algorithms which have small, but non-constant competitive factors. They proposed tango, a BST algorithm which is nearly dynamically optimal -- its competitive ratio is O(log log n) instead of a constant. Unfortunately, for many access patterns, tango is worse than other BST algorithms by a factor of log log n. In this paper we introduce multi-splay trees, which can be viewed as a variant of splay trees. We prove the multi-splay access lemma, which resembles the access lemma for splay trees. With different assignment of weights, this lemma allows us to prove various bounds on the performance of multi-splay trees. Specifically, we prove that multi-splay trees are O(log log n)-competitive, and amortized O(log n). This is the first BST data structure to simultaneously achieve these two bounds. In addition, the algorithm is simple enough that we include code for its key parts."

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