Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Popular Matching in Roommates Setting is NP-hard   An input to the Popular Matching problem, in the roommates setting, consists
of a graph $G$ and each vertex ranks its neighbors in strict order, known as
its preference. In the Popular Matching problem the objective is to test
whether there exists a matching $M^\star$ such that there is no matching $M$
where more people are happier with $M$ than with $M^\star$. In this paper we
settle the computational complexity of the Popular Matching problem in the
roommates setting by showing that the problem is NP-complete. Thus, we resolve
an open question that has been repeatedly, explicitly asked over the last
decade.

11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex