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Lower bounds for set intersection queries

Author: Paul Frederick Dietz; Max-Planck-Institut für Informatik.
Publisher: Saarbrücken, Germany : Max-Planck-Institut für Informatik, [1992]
Edition/Format:   book_printbook : EnglishView all editions and formats
Database:WorldCat
Summary:
Abstract: "We consider the following set intersection reporting problem. We have a collection of initially empty sets and would like to process an intermixed sequence of n updates (insertions into and deletions from individual sets) and q queries (reporting the intersection of two sets). We cast this problem in the arithmetic model of computation of Fredman [Fre81] and Yao [Yao85] and show that any algorithm that
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Document Type: Book
All Authors / Contributors: Paul Frederick Dietz; Max-Planck-Institut für Informatik.
OCLC Number: 30542416
Notes: "October 1992."
"MPI-I-92-127."
Description: 14 leaves ; 30 cm
Responsibility: P. Dietz [and others].

Abstract:

Abstract: "We consider the following set intersection reporting problem. We have a collection of initially empty sets and would like to process an intermixed sequence of n updates (insertions into and deletions from individual sets) and q queries (reporting the intersection of two sets). We cast this problem in the arithmetic model of computation of Fredman [Fre81] and Yao [Yao85] and show that any algorithm that fits in this model must take time [omega](q + n[square root of]q) to process a sequence of n updates and q queries, ignoring factors that are polynomial in log n. We show that this bound is tight in this model of computation, again to within a polynomial in log n factor, improving upon a result of Yellin [Yel92].

Furthermore we consider the case q = O(n) with an additional space restriction. We only allow to use m memory locations, where m [<or =] n[superscript 3/2]. We show a tight bound of [theta](n²m[superscript 1/3]) for a sequence of O(n) operations, again ignoring polynomial in log n factors."

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