Boolean Matrix Multiplication (Combinatorial): Difference between revisions
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(Created page with "{{DISPLAYTITLE:Boolean Matrix Multiplication (Combinatorial) (Matrix Product)}} == Description == Matrix multiplication of two boolean matrices (i.e. where all entries are in $F_2$ and addition is mod 2). Here, only "combinatorial" algorithms are considered. == Related Problems == Generalizations: Boolean Matrix Multiplication Related: Matrix Multiplication, Matrix Product Verification, Distance Product, $(\min, \leq)$ Product == Parameters ==...") |
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== Parameters == | == Parameters == | ||
$n$: dimension of square matrix | |||
== Table of Algorithms == | == Table of Algorithms == | ||
Latest revision as of 08:18, 10 April 2023
Description
Matrix multiplication of two boolean matrices (i.e. where all entries are in $F_2$ and addition is mod 2). Here, only "combinatorial" algorithms are considered.
Related Problems
Generalizations: Boolean Matrix Multiplication
Related: Matrix Multiplication, Matrix Product Verification, Distance Product, $(\min, \leq)$ Product
Parameters
$n$: dimension of square matrix
Table of Algorithms
| Name | Year | Time | Space | Approximation Factor | Model | Reference |
|---|---|---|---|---|---|---|
| 2018 | $O(n^{3} / log^{2.25} n)$ | Exact | Deterministic | Time | ||
| Method of Four Russians | 1970 | $O(n^{3}/(log n)$^{2}) | Exact | Deterministic | Time | |
| Bansal, Williams | 2009 | $O(n^{3} * (log log n)$^{2} / log^{2.25} n) | Exact | Randomized | Time | |
| Bansal, Williams | 2009 | $O(n^{3} * (log log n)$^{2} / (w * (log n)^{7}/{6})) | Exact | Randomized | Time | |
| Chan | 2015 | $O(n^{3} * (log log n)$^{3} / log^{3} n) | Exact | Deterministic | Time | |
| Chan | 2015 | $O(n^{3} * (log w)$^{3} / (w * log^{2} n)) | Exact | Deterministic | Time | |
| Yu | 2015 | $O(n^{3}*poly(log log n)$/log^{4} n) | Exact | Deterministic | Time |
References/Citation
https://www.sciencedirect.com/science/article/pii/S0890540118300099