Chen, J., & Csáji, G. (2023). Optimal Capacity Modification for Many-To-One Matching Problems. In Proceedings of the 2023 International Conference on Autonomous Agents and Multiagent Systems (pp. 2880–2882).
E192-01 - Forschungsbereich Algorithms and Complexity
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Published in:
Proceedings of the 2023 International Conference on Autonomous Agents and Multiagent Systems
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ISBN:
978-1-4503-9432-1
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Date (published):
2023
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Event name:
22nd International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2023)
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Event date:
29-May-2023 - 2-Jun-2023
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Event place:
London, United Kingdom of Great Britain and Northern Ireland (the)
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Number of Pages:
3
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Peer reviewed:
Yes
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Keywords:
School choice; Stable matching; Pareto-efficient matching; Parameterized complexity
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Approximation algorithms
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Abstract:
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 MinSum) and the other aiming to minimize the maximum capacity increase of any school (abbrv. as MinMax). We obtain a complete picture in terms of computational complexity: Except for stable and perfect matchings using the MinMax 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 Pareto-efficient matchings via minimal capacity increases is much harder than achieving stable and perfect matchings.
