Capacity Variation in the Many-to-one Stable Matching

Bobbio, Federico; Carvalho, Margarida; Lodi, Andrea; Torrico, Alfredo

doi:10.48550/arxiv.2205.01302

Cited by 2 publications

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“…Nguyen and Vohra [24] studied many-toone matching with couples and propose algorithms to find a stable matching by perturbing the capacities. Bobbio et al [6,7] considered capacity variations to obtain a stable matching with minimum average rank of the matched schools (A R…”

Section: Students Schoolsmentioning

confidence: 99%

Optimal Capacity Modification for Many-To-One Matching Problems

Csáji¹

2023

Preprint

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We consider many-to-one matching problems, where one side consists of students and the other side of schools with capacity constraints. We study how to optimally increase the capacities of the schools so as to obtain a stable and perfect matching (i.e., every student is matched) or a matching that is stable and Pareto-efficient for the students. We consider two common optimality criteria, one aiming to minimize the sum of capacity increases of all schools (abbrv. as M S ) and the other aiming to minimize the maximum capacity increase of any school (abbrv. as M M ). We obtain a complete picture in terms of computational complexity: Except for stable and perfect matchings using the M M criteria which is polynomial-time solvable, all three remaining problems are NP-hard. We further investigate the parameterized complexity and approximability and find that achieving stable and Paretoefficient matchings via minimal capacity increases is much harder than achieving stable and perfect matchings.

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Section: Students Schoolsmentioning

confidence: 99%