## A Time-Space Tradeoff for Boolean Matrix Multiplication

Citations: | 7 - 0 self |

### BibTeX

@MISC{Abrahamson_atime-space,

author = {Karl Abrahamson},

title = { A Time-Space Tradeoff for Boolean Matrix Multiplication},

year = {}

}

### Years of Citing Articles

### OpenURL

### Abstract

A time-space tradeoff is established in the branching program model for the problem of computing the product of two n x n matrices over the semiring ((0, l}, V, A). It is a.ssumed that ea.ch element of each nxn input matrix is chosen independently to be 1 with probability n-ll2 and to be 0 with probability 1- n-1/2. Letting S and T denote expected space and time of a deterministic algorithm, the tradeoff is ST = R(n3.5) for T < cln2.5 and ST = R(n3) for T> where c1, c2> 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 a.t T = O(n2.5). These expected case lower bounds are also the best known lower bounds for the worst case.