Self-adjusting binary search trees
Journal of the ACM (JACM)
Lower bounds for accessing binary search trees with rotations
SIAM Journal on Computing
Elements of information theory
Elements of information theory
An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
Alternatives to splay trees with O(log n) worst-case access times
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
On paging with locality of reference
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
The Art of Computer Programming, 2nd Ed. (Addison-Wesley Series in Computer Science and Information
The Art of Computer Programming, 2nd Ed. (Addison-Wesley Series in Computer Science and Information
On the Dynamic Finger Conjecture for Splay Trees. Part I: Splay Sorting log n-Block Sequences
SIAM Journal on Computing
On the Dynamic Finger Conjecture for Splay Trees. Part II: The Proof
SIAM Journal on Computing
Journal of Logic, Language and Information
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
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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 @W(m(logn-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.