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- W2783505302 abstract "In this paper we propose models of combinatorial algorithms for the Boolean Matrix Multiplication (BMM), and prove lower bounds on computing BMM in these models. First, we give a relatively relaxed combinatorial model which is an extension of the model by Angluin (1976), and we prove that the time required by any algorithm for the BMM is at least $Omega(n^3 / 2^{O( sqrt{ log n })})$. Subsequently, we propose a more general model capable of simulating the Four Russians Algorithm. We prove a lower bound of $Omega(n^{7/3} / 2^{O(sqrt{ log n })})$ for the BMM under this model. We use a special class of graphs, called $(r,t)$-graphs, originally discovered by Rusza and Szemeredi (1978), along with randomization, to construct matrices that are hard instances for our combinatorial models." @default.
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- W2783505302 date "2018-01-16" @default.
- W2783505302 modified "2023-09-23" @default.
- W2783505302 title "Lower bounds for Combinatorial Algorithms for Boolean Matrix Multiplication" @default.
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