Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Subcubic Equivalences Between Graph Centrality Measures and
  Complementary Problems   Despite persistent efforts, there is no known technique for obtaining
unconditional super-linear lower bounds for the computational complexity of the
problems in P. Vassilevska Williams and Williams introduce a fruitful approach
to advance a better understanding of the computational complexity of the
problems in P. In particular, they consider All Pairs Shortest Paths (APSP) and
other fundamental problems such as checking whether a matrix defines a metric,
verifying the correctness of a matrix product, and detecting a negative
triangle in a graph. Abboud, Grandoni, and Vassilevska Williams study
well-known graph centrality problems such as Radius, Median, etc., and make a
connection between their computational complexity to that of two fundamental
problems, namely APSP and Diameter. They show any algorithm with subcubic
running time for these centrality problems, implies a subcubic algorithm for
either APSP or Diameter. In this paper, we define vertex versions for these
centrality problems and based on that we introduce new complementary problems.
The main open problem of Abboud et al. is whether or not APSP and Diameter are
equivalent under subcubic reduction. One of the results of this paper is APSP
and CoDiameter, which is the complementary version of Diameter, are equivalent.
Moreover, for some of the problems in this set, we show that they are
equivalent to their complementary versions. Considering the slight difference
between a problem and its complementary version, these equivalences give us the
impression that every problem has such a property, and thus APSP and Diameter
are equivalent. This paper is a step forward in showing a subcubic equivalence
between APSP and Diameter, and we hope that the approach introduced in our
paper can be helpful to make this breakthrough happen.

11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
2
The categories of this paper are: math