Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficient algorithms for three-dimensional axial and planar random
  assignment problems   Beautiful formulas are known for the expected cost of random two-dimensional
assignment problems, but in higher dimensions even the scaling is not known. In
three dimensions and above, the problem has natural "Axial" and "Planar"
versions, both of which are NP-hard. For 3-dimensional Axial random assignment
instances of size $n$, the cost scales as $\Omega(1/n)$, and a main result of
the present paper is a linear-time algorithm that, with high probability, finds
a solution of cost $O(n^{-1+o(1)})$. For 3-dimensional Planar assignment, the
lower bound is $\Omega(n)$, and we give a new efficient matching-based
algorithm that with high probability returns a solution with cost $O(n \log
n)$.

30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol