Lower bound techniques for data structures
Name
320089443-MIT.pdf
Description
Full printable version
Size
12.15 MB
Format
Adobe PDF
Checksum (MD5)
e09d11d33ac967e80d538a0ddc5d072e
Author(s)
Pǎtraşcu, Mihai
Advisor(s)
Erik D. Demaine.
Date Issued
2008
Publisher
Massachusetts Institute of Technology
Abstract
We describe new techniques for proving lower bounds on data-structure problems, with the following broad consequences: * the first [omega](lg n) lower bound for any dynamic problem, improving on a bound that had been standing since 1989; * for static data structures, the first separation between linear and polynomial space. Specifically, for some problems that have constant query time when polynomial space is allowed, we can show [omega](lg n/ lg lg n) bounds when the space is O(n - polylog n). Using these techniques, we analyze a variety of central data-structure problems, and obtain improved lower bounds for the following: * the partial-sums problem (a fundamental application of augmented binary search trees); * the predecessor problem (which is equivalent to IP lookup in Internet routers); * dynamic trees and dynamic connectivity; * orthogonal range stabbing. * orthogonal range counting, and orthogonal range reporting; * the partial match problem (searching with wild-cards); * (1 + [epsilon])-approximate near neighbor on the hypercube; * approximate nearest neighbor in the l[infinity] metric. Our new techniques lead to surprisingly non-technical proofs. For several problems, we obtain simpler proofs for bounds that were already known.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.
Includes bibliographical references (p. 135-143).
Subjects
Electrical Engineering and Computer Science.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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