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Cell-Probe Proofs

Published:01 November 2010Publication History
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Abstract

We study the nondeterministic cell-probe complexity of static data structures. We introduce cell-probe proofs (CPP), a proof system for the cell-probe model, which describes verification instead of computation in the cell-probe model. We present a combinatorial characterization of CPP. With this novel tool, we prove the following lower bounds for the nondeterministic cell-probe complexity of static data structures.

–There exists a data structure problem with high nondeterministic cell-probe complexity.

–For the exact nearest neighbor search (NNS) problem or the partial match problem in high dimensional Hamming space, for any data structure with Poly(n) cells, each of which contains O(nC) bits where C < 1, the nondeterministic cell-probe complexity is at least Ω(log(d/log n)), where d is the dimension and n is the number of points in the data set.

–For the polynomial evaluation problem of d-degree polynomial over finite field of size 2k where d ≤ 2k, for any data structure with s cells, each of which contains b bits, the nondeterministic cell-probe complexity is at least min ((k/b (d − 1)), (k−log(d−1)/logs)).

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              • Published in

                cover image ACM Transactions on Computation Theory
                ACM Transactions on Computation Theory  Volume 2, Issue 1
                November 2010
                42 pages
                ISSN:1942-3454
                EISSN:1942-3462
                DOI:10.1145/1867719
                Issue’s Table of Contents

                Copyright © 2010 ACM

                Publisher

                Association for Computing Machinery

                New York, NY, United States

                Publication History

                • Published: 1 November 2010
                • Revised: 1 February 2010
                • Accepted: 1 February 2010
                • Received: 1 October 2008
                Published in toct Volume 2, Issue 1

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