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

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.Comment: 30 pages, 1 figure. Reason for update: additional discussion on the Kemeny Score problem, and correction of some typo

Stable Matchings with Covering Constraints: A Complete Computational Trichotomy

Stable matching problems with lower quotas are fundamental in academic hiring andensuring operability of rural hospitals. Only few tractable (polynomial-time solvable)cases of stable matching with lower quotas have been identified; most such problemsareNP-hard and also hard to approximate (Hamada et al. in Algorithmica 74(1):440–465, 2016). We therefore consider stable matching problems with lower quotas under arelaxed notion of tractability, namely fixed-parameter tractability. By cloning hospitalswe focus on the case when all hospitals have upper quota equal to 1, which general-izes the setting of “arranged marriages” first considered by Knuth (Mariages stableset leurs relations avec d’autres problèmes combinatoires, Les Presses de l’Universitéde Montréal, Montreal, 1976). We investigate how a set of natural parameters, namelythe maximum length of preference lists for men and women, the number of distin-guished men and women, and the number of blocking pairs allowed determine thecomputational tractability of this problem. Our main result is a complete complexitytrichotomy: for each choice of parameters we either provide a polynomial-time algo-rithm, or anNP-hardness proof and fixed-parameter algorithm, orNP-hardness proofandW[1]-hardness proof. As corollary, we negatively answer a question by Hamadaet al. (Algorithmica 74(1):440–465, 2016) by showing fixed-parameter intractabil-ity parameterized by optimal solution size. We also classify all cases of one-sidedconstraints where only women may be distinguished

Considering stakeholders’ preferences for scheduling slots in capacity constrained airports

Airport slot scheduling has attracted the attention of researchers as a capacity management tool at congested airports. Recent research work has employed multi-objective approaches for scheduling slots at coordinated airports. However, the central question on how to select a commonly accepted airport schedule remains. The various participating stakeholders may have multiple and sometimes conflicting objectives stemming from their decision-making needs. This complex decision environment renders the identification of a commonly accepted solution rather difficult. In this presentation, we propose a multi-criteria decision-making technique that incorporates the priorities and preferences of the stakeholders in order to determine the best compromise solution

LIPIcs, Volume 244, ESA 2022, Complete Volume

LIPIcs, Volume 244, ESA 2022, Complete Volum