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=Θ(logl+(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 Θ(n 1/l) ≤ S(n,l) ≤ O(ln 1/l).
Supported in part by the National Science Foundation under grant MIP-86-02256 and by the Joint Services Electronics Program under contract F49620-87-C0044.
Work done while at Cornell University was supported in part by the National Science Foundation under grant DCR-86-02307
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© 1989 Springer-Verlag Berlin Heidelberg
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Bilardi, G., Moitra, A. (1989). Time lower bounds for CREW-PRAM computation of monotone functions. In: Ausiello, G., Dezani-Ciancaglini, M., Della Rocca, S.R. (eds) Automata, Languages and Programming. ICALP 1989. Lecture Notes in Computer Science, vol 372. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0035754
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DOI: https://doi.org/10.1007/BFb0035754
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