The cost of offline binary search tree algorithms and the complexity of the request sequence

In evaluating the performance of online algorithms for search trees, one wants to compare them to the best offline algorithm available. In this paper we lower bound the cost of an optimal offline binary search tree using the Kolmogorov complexity of the request sequence. We obtain several applicatio...

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Bibliographic Details
Published in:Theoretical computer science Vol. 393; no. 1; pp. 231 - 239
Main Authors: Kujala, Jussi, Elomaa, Tapio
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 20.03.2008
Elsevier
Subjects:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Combinatorics
Combinatorics. Ordered structures
Computer science; control theory; systems
Exact sciences and technology
Graph theory
Kolmogorov complexity
Mathematics
Miscellaneous
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in probability and statistics
Offline binary search tree algorithms
Sciences and techniques of general use
Splay trees
Theoretical computing
Offline binary search tree algorithms
Splay trees
Kolmogorov complexity
Lower bound
Costs
Computer theory
Online algorithm
Entropy
Search algorithm
Markov chain
Binary tree
Binary search tree
Algorithm complexity
Search tree
Performance
Application
ISSN:0304-3975, 1879-2294
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Summary:In evaluating the performance of online algorithms for search trees, one wants to compare them to the best offline algorithm available. In this paper we lower bound the cost of an optimal offline binary search tree using the Kolmogorov complexity of the request sequence. We obtain several applications for this result. First, any offline binary search tree algorithm can be at most a constant factor away from the entropy of the process producing the request sequence. Second, for a fraction 1 − 1 / 2 m of request sequences of length m on n items the cost of any offline algorithm is Ω ( m ( log n − 1 ) ) . Third, the expected cost of splay trees is within a constant factor of the expected cost of an optimal offline binary search tree algorithm in a subset of Markov chains.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2007.12.015