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- W2810352927 abstract "The Boolean product $R = P cdot Q$ of two ${ 0, 1} ; m times m ; $ matrices is $$R(j,k) = 1 ; mathrm{ IF some } ; t ; ,P(j, t) = Q(t, k) = 1; ; mathrm{ELSE } , R(j, k) = 0. $$ The near-optimal design reduces the complexity of computing $R$ from the standard $m^3$ to $O(m^{(2+e)})$, for arbitrary small $e > 0$, by a practical algorithm. This renders reduced complexity to several graph-property tests: Finding triangles and higher-size cliques; finding all-pairs shortest paths, and more. Also, parsing a string $w$ by a context-free grammar is reduced to near quadratic in $w$-size. The design uses several distinct 2-digit encodings: $j$ by $(j_1, j_2), ; k , $ by $, (k_1, k_2)$. Each one gives rise to bunches of short digraphs from sources $j$'s to sinks $k$'s via switching nodes, and walks between them. The combined information, using the Chinese remainder theorem, leads to the correct values of $R(j, k)$." @default.
- W2810352927 created "2018-07-10" @default.
- W2810352927 creator A5056190255 @default.
- W2810352927 date "2018-06-23" @default.
- W2810352927 modified "2023-09-27" @default.
- W2810352927 title "Almost optimal Boolean matrix multiplication [BMM]-by multi-encoding of rows and columns" @default.
- W2810352927 hasPublicationYear "2018" @default.
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