Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polynomially tractable cases in the popular roommates problem   The input of the popular roommates problem consists of a graph $G = (V, E)$
and for each vertex $v\in V$, strict preferences over the neighbors of $v$.
Matching $M$ is more popular than $M'$ if the number of vertices preferring $M$
to $M'$ is larger than the number of vertices preferring $M'$ to $M$. A
matching $M$ is called popular if there is no matching $M'$ that is more
popular than $M$.
  Only recently Faenza et al. and Gupta et al. resolved the long-standing open
question on the complexity of deciding whether a popular matching exists in a
popular roommates instance and showed that the problem is NP-complete. In this
paper we identify a class of instances that admit a polynomial-time algorithm
for the problem. We also test these theoretical findings on randomly generated
instances to determine the existence probability of a popular matching in them.

18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
2
The categories of this paper are: math
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat