Optimal Preprocessing for Answering On-Line Product Queries
Noga Alon, Baruch Schieber

TL;DR
This paper investigates the optimal preprocessing strategies for fast online product queries in semigroups and trees, establishing tight bounds and efficient parallel algorithms with broad applications.
Contribution
It introduces tight bounds for preprocessing time and space to answer product queries in semigroups and trees, and develops optimal parallel algorithms for these problems.
Findings
Preprocessing of Θ(n λ(k,n)) is necessary and sufficient for k-step query answering.
Linear preprocessing enables O(α(n)) query time, which is proven optimal.
Parallel algorithms run in O(log n) time and are optimal in total operations.
Abstract
We examine the amount of preprocessing needed for answering certain on-line queries as fast as possible. We start with the following basic problem. Suppose we are given a semigroup . Let be elements of . We want to answer on-line queries of the form, ``What is the product ?'' for any given . We show that a preprocessing of time and space is both necessary and sufficient to answer each such query in at most steps, for any fixed . The function is the inverse of a certain function at the -th level of the primitive recursive hierarchy. In case linear preprocessing is desired, we show that one can answer each such query in steps and that this is best possible. The function is the…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsSemantic Web and Ontologies · Data Management and Algorithms · Advanced Database Systems and Queries
