Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Polynomial-Time Algorithm for Unconstrained Binary Quadratic
  Optimization   In this paper, an exact algorithm in polynomial time is developed to solve
unrestricted binary quadratic programs. The computational complexity is
$O\left( n^{\frac{15}{2}}\right) $, although very conservative, it is
sufficient to prove that this minimization problem is in the complexity class
$P$. The implementation aspects are also described in detail with a special
emphasis on the transformation of the quadratic program into a linear program
that can be solved in polynomial time. The algorithm was implemented in MATLAB
and checked by generating five million matrices of arbitrary dimensions up to
30 with random entries in the range $\left[ -50,50\right] $. All the
experiments carried out have revealed that the method works correctly.

4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th