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

Ildikó Schlotter

Abstract: A preference system I<math><mi mathvariant="script" is="true">I</mi></math> is an undirected graph where vertices have preferences over their neighbors, and I<math><mi mathvariant="script" is="true">I</mi></math> 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 I<math><mi mathvariant="script" is="true">I</mi></math> is close to admitting a master list based on three different distance measures. We determine the computational complexity of the following questions: can I<math><mi mathvariant="script" is="true">I</mi></math> 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.