A time-space tradeoff for Boolean matrix multiplication

A time-space tradeoff is established in the branching program model for the problem of computing the product of two n*n matrices over a certain semiring. It is assumed that each element of each n*n input matrix is chosen independently to be 1 with probability n/sup -1/2/ and to be 0 with probability...

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Bibliographic Details
Published inProceedings [1990] 31st Annual Symposium on Foundations of Computer Science pp. 412 - 419 vol. 1
Main Author Abrahamson, K.
Format Conference Proceeding
LanguageEnglish
Published IEEE Comput. Soc. Press 1990
Subjects
Binary decision diagrams
Computational modeling
Computer science
Equations
Polynomials
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Summary:A time-space tradeoff is established in the branching program model for the problem of computing the product of two n*n matrices over a certain semiring. It is assumed that each element of each n*n input matrix is chosen independently to be 1 with probability n/sup -1/2/ and to be 0 with probability 1-n/sup -1/2/. Letting S and T denote expected space and time of a deterministic algorithm, the tradeoff is ST= Omega (n/sup 3.5/) for T<c/sub 1/n/sup 2.5 /and ST Omega (n/sup 3/) for T<c/sub 2/n/sup 2.5/, where c/sub 1/,/sub /c/sub 2/ >0. The lower bounds are matched to within a logarithmic factor by upper bounds in the branching program model. Thus, the tradeoff possesses a sharp break at T= Theta (n/sup 2.5/). These expected case lower bounds are also the best known lower bounds for the worst case.< >
ISBN:081862082X
9780818620829
DOI:10.1109/FSCS.1990.89561