Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stable Marriage with Covering Constraints: A Complete Computational
  Trichotomy   We consider Stable Marriage with Covering Constraints (SMC): in this variant
of Stable Marriage, we distinguish a subset of women as well as a subset of
men, and we seek a matching with fewest number of blocking pairs that matches
all of the distinguished people. We investigate how a set of natural
parameters, namely the maximum length of preference lists for men and women,
the number of distinguished men and women, and the number of blocking pairs
allowed determine the computational tractability of this problem. Our main
result is a complete complexity trichotomy that, for each choice of the studied
parameters, classifies SMC as polynomial-time solvable, NP-hard and
fixed-parameter tractable, or NP-hard and W[1]-hard. We also classify all cases
of one-sided constraints where only women may be distinguished.

17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol