Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Improved Upper Bound on Maximal Clique Listing via Rectangular Fast
  Matrix Multiplication   The first output-sensitive algorithm for the Maximal Clique Listing problem
was given by Tsukiyama et.al. in 1977. As any algorithm falling within the
Reverse Search paradigm, it performs a DFS visit of a directed tree (the
RS-tree) having the objects to be listed (i.e. maximal cliques) as its nodes.
In a recursive implementation, the RS-tree corresponds to the recursion tree of
the algorithm. The time delay is given by the cost of generating the next child
of a node, and Tsukiyama showed it is $O(mn)$. In 2004, Makino and Uno
sharpened the time delay to $O(n^{\omega})$ by generating all the children of a
node in one single shot performed by computing a \emph{square} fast matrix
multiplication. In this paper, we further improve the asymptotics for the
exploration of the same RS-tree by grouping the offsprings' computation even
further. Our idea is to rely on rectangular fast matrix multiplication in order
to compute all children of $n^2$ nodes in one shot. According to the current
upper bounds on fast matrix multiplication, with this the time delay improves
from $O(n^{2.3728639})$ to $O(n^{2.093362})$.

23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
2
The categories of this paper are: math
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc