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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 −doi:10.1016/j.tcs.2007.12.015 fatcat:27dk2gehqfce3hzvefpowmtpyq