Time-space tradeoffs for set operations

Boaz Patt-Shamir, David Peleg

Research output: Contribution to journalArticlepeer-review

Abstract

This paper considers time-space tradeoffs for various set operations. Denoting the time requirement of an algorithm by T and its space requirement by S, it is shown that TS=Ω(n2) for set complementation and TS=Ω(n 3 2) for set intersection, in the R-way branching program model. In the more restricted model of comparison branching programs, the paper provides two additional types of results. A tradeoff of TS=Ω(n2-ε(n)), derived from Yao's lower bound for element distinctness, is shown for set disjointness, set union and set intersection [where ε(n)=O((logn)- 1 2)]. A bound of TS=Ω(n 3 2) is shown for deciding set equality and set inclusion. Finally, a classification of set operations is presented, and it is shown that all problems of a large naturally arising class are as hard as the problems bounded in this paper.

Original languageEnglish
Pages (from-to)99-129
Number of pages31
JournalTheoretical Computer Science
Volume110
Issue number1
DOIs
StatePublished - 15 Mar 1993
Externally publishedYes

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