Are there any nicely structured preference profiles nearby?

Robert Bredereck; Jiehua Chen; Gerhard J. Woeginger

doi:10.1016/j.mathsocsci.2015.11.002

Are there any nicely structured preference profiles nearby?

Robert Bredereck, Jiehua Chen, Gerhard J. Woeginger

Research output: Contribution to journal › Article › peer-review

36 Scopus citations

Abstract

We investigate the problem of deciding whether a given preference profile is close to having a certain nice structure, as for instance single-peaked, single-caved, single-crossing, value-restricted, best-restricted, worst-restricted, medium-restricted, or group-separable profiles. We measure this distance by the number of voters or alternatives that have to be deleted to make the profile a nicely structured one. Our results classify the problem variants with respect to their computational complexity, and draw a clear line between computationally tractable (polynomial-time solvable) and computationally intractable (NP-hard) questions.

Original language	English
Pages (from-to)	61-73
Number of pages	13
Journal	Mathematical Social Sciences
Volume	79
DOIs	https://doi.org/10.1016/j.mathsocsci.2015.11.002
State	Published - 1 Jan 2016
Externally published	Yes

ASJC Scopus subject areas

Sociology and Political Science
Social Sciences (all)
Psychology (all)
Statistics, Probability and Uncertainty

Access to Document

10.1016/j.mathsocsci.2015.11.002

Cite this

@article{97e1c0be4aec40c5b60670d73e44a33f,

title = "Are there any nicely structured preference profiles nearby?",

abstract = "We investigate the problem of deciding whether a given preference profile is close to having a certain nice structure, as for instance single-peaked, single-caved, single-crossing, value-restricted, best-restricted, worst-restricted, medium-restricted, or group-separable profiles. We measure this distance by the number of voters or alternatives that have to be deleted to make the profile a nicely structured one. Our results classify the problem variants with respect to their computational complexity, and draw a clear line between computationally tractable (polynomial-time solvable) and computationally intractable (NP-hard) questions.",

author = "Robert Bredereck and Jiehua Chen and Woeginger, {Gerhard J.}",

note = "Funding Information: The first author was supported by the DFG project PAWS (NI 369/10). The second author was supported by the Studienstiftung des Deutschen Volkes . The third author was supported by the Alexander von Humboldt Foundation . We are very grateful to the reviewers of this article and its conference version Bredereck et al., 2013b at IJCAI 2013 for their detailed and constructive feedback. Publisher Copyright: {\textcopyright} 2015 Elsevier B.V.",

year = "2016",

month = jan,

day = "1",

doi = "10.1016/j.mathsocsci.2015.11.002",

language = "English",

volume = "79",

pages = "61--73",

journal = "Mathematical Social Sciences",