Recognizing When a Preference System is Close to Admitting a Master List

Schlotter, Ildikó Anna (2023) Recognizing When a Preference System is Close to Admitting a Master List. In: WALCOM: Algorithms and Computation : 17th International Conference and Workshops, WALCOM 2023, Hsinchu, Taiwan, March 22–24, 2023, Proceedings. Lecture Notes in Computer Science (13973). Springer Cham, pp. 317-329. ISBN 978-3-031-27050-5 (nyomtatott)

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Abstract

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 dierent distance measures. We determine the computational complexity of the following questions: can I be modied 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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