# OPTIMAL PREPROCESSING FOR S ANSWERING ON-LINE PRODUCT QUERIE

@inproceedings{Alon1987OPTIMALPF, title={OPTIMAL PREPROCESSING FOR S ANSWERING ON-LINE PRODUCT QUERIE}, author={Noga Alon and Baruch Schieber}, year={1987} }

e q We examine the amount of preprocessing needed for answering certain on-lin ueries as fast as possible. We start with the following basic problem. Suppose we are e given a semigroup (S ,°). Let s , . . . , s be elements of S . We want to answer on-lin 1 n i i +1 j −1 j n 1 queries of the form, "What is the product s °s ° . . . °s °s ?" for any give ≤ i ≤ j ≤ n . We show that a preprocessing of Θ(n λ(k ,n )) time and space is both . T necessary and sufficient to answer each such query in at…

## 19 Citations

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