Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stable Roommates with Narcissistic, Single-Peaked, and Single-Crossing
  Preferences   The classical Stable Roommates problem is to decide whether there exists a
matching of an even number of agents such that no two agents which are not
matched to each other would prefer to be with each other rather than with their
respectively assigned partners. We investigate Stable Roommates with complete
(i.e., every agent can be matched with any other agent) or incomplete
preferences, with ties (i.e., two agents are considered of equal value to some
agent) or without ties. It is known that in general allowing ties makes the
problem NP-complete. We provide algorithms for Stable Roommates that are,
compared to those in the literature, more efficient when the input preferences
are complete and have some structural property, such as being narcissistic,
single-peaked, and single-crossing. However, when the preferences are
incomplete and have ties, we show that being single-peaked and single-crossing
does not reduce the computational complexity--Stable Roommates remains
NP-complete.

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The categories of this paper are: math
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: physics
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The categories of this paper are: atom-ph