Are there any nicely structured preference profiles nearby?

Authors:
Robert Bredereck;Jiehua Chen;Gerhard J. Woeginger
Affiliations:
TU Berlin, Germany;TU Berlin, Germany;TU Eindhoven, Netherlands
Venue:
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Year:
2013

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Abstract

We investigate the problem of deciding whether a given preference profile is close to a nicely structured preference profile of a certain type, as for instance single-peaked, single-caved, singlecrossing, 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 so as to reach a nicely structured profile. Our results classify all considered 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.