Time Lower Bounds for CREW-PRAM Computation of Monotone Functions

Other Titles
Abstract

It is shown that the time to compute a monotone boolean function depending upon n variables on a CREW-PRAM satisfies the lower bound T=Ω(log l + (log n)/l), where l is the size of the largest prime implicant. It is also shown that the bound is existentially tight by constructing a family of monotone functions that can be computed in T=O(log l + (log n)/l), even by an EREW-PRAM. The same results hold if l is replaced by L, the size of the largest prime clause. An intermediate result of independent interest is that S(n,l), the size of the largest minimal vertex cover minimized over all (reduced) hypergraphs of n vertices and maximum hyperedge size l, satisfies the bounds Ω(n1/l)≤S(n,l)≤O(ln1/l).

Journal / Series
Volume & Issue
Description
Sponsorship
Date Issued
1989-05
Publisher
Cornell University
Keywords
computer science; technical report
Location
Effective Date
Expiration Date
Sector
Employer
Union
Union Local
NAICS
Number of Workers
Committee Chair
Committee Co-Chair
Committee Member
Degree Discipline
Degree Name
Degree Level
Related Version
Related DOI
Related To
Related Part
Based on Related Item
Has Other Format(s)
Part of Related Item
Related To
Related Publication(s)
Link(s) to Related Publication(s)
References
Link(s) to Reference(s)
Previously Published As
http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR89-1012
Government Document
ISBN
ISMN
ISSN
Other Identifiers
Rights
Rights URI
Types
technical report
Accessibility Feature
Accessibility Hazard
Accessibility Summary
Link(s) to Catalog Record