WALCOM: Algorithms and Computation
© 17th International Conference and Workshops, WALCOM 2023, Hsinchu, Taiwan, March 22–24, 2023, conference proceedings
Part of the book series:Lecture Notes in Computer Science (LNCS, volume 13973)
Recognizing When a Preference System is Close to Admitting a Master List
A preference system I is an undirected graph where vertices have preferences over their neighbors, and 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 I is close to admitting a master list based on three different distance measures. We determine the computational complexity of the following questions: can 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.
Supported by the Hungarian Academy of Sciences under its Momentum Programme (LP2021-2) and the Hungarian Scientific Research Fund (OTKA grants K128611 and K124171).