Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Improved algorithms for Boolean matrix multiplication via opportunistic
  matrix multiplication   Karppa & Kaski (2019) proposed a novel type of "broken" or "opportunistic"
multiplication algorithm, based on a variant of Strassen's alkgorithm, and used
this to develop new algorithms for Boolean matrix multiplication, among other
tasks. For instance, their algorithm can compute Boolean matrix multiplication
in $O(n^{\log_2(6 + 6/7)} \log n) = O(n^{2.778})$ time. While faster matrix
multiplication algorithms exist asymptotically, in practice most such
algorithms are infeasible for practical problems. Their opportunistic algorithm
is a slight variant of Strassen's algorithm, so hopefully it should yield
practical as well as asymptotic improvements to it.
  In this note, we describe a more efficient way to use the broken matrix
multiplication algorithm to solve Boolean matrix multiplication. In brief,
instead of running multiple iterations of the broken algorithm on the original
input matrix, we form a new larger matrix by sampling and run a single
iteration of the broken algorithm on it. The resulting algorithm has runtime
$O( n^{\frac{3 \log 6}{\log 7}} (\log n)^{\frac{ \log 6}{\log 7}}) \leq
O(n^{2.763})$. We also describe an extension to witnessing Boolean matrix
multiplication, as well as extensions to non-square matrices.
  The new algorithm is simple and has reasonable constants. We hope it may lead
to improved practical algorithms

24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int