Recognizing when a preference system is close to admitting a master list

Ildikó Schlotter

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arXiv · 2212.03521

Recognizing when a preference system is close to admitting a master list

Ildikó Schlotter

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Abstract

A preference system $\mathcal{I}$ is an undirected graph where vertices have preferences over their neighbors, and $\mathcal{I}$ admits a master list if all preferences can be derived from a single ordering over all vertices. We study the problem of deciding whether a given preference system $\mathcal{I}$ is close to admitting a master list based on three different distance measures. We determine the computational complexity of the following questions: can $\mathcal{I}$ be modified by (i) $k$ swaps in the preferences, (ii) $k$ edge deletions, or (iii) $k$ vertex deletions so that the resulting instance admits a master list? We investigate these problems in detail from the viewpoint of parameterized complexity and of approximation. We also present two applications related to stable and popular matchings.

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Ildikó Schlotter. 2022-12-07. Recognizing when a preference system is close to admitting a master list. https://arxiv.org/abs/2212.03521

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