An Approximation Algorithm for Maximum Stable Matching with Ties and Constraints
We present a polynomial-time 3/2-approximation algorithm for the problem of finding a maximum-cardinality stable matching in a many-to-many matching model with ties and laminar constraints on both sides. We formulate our problem using a bipartite multigraph whose vertices are called workers and firms, and edges are called contracts. Our algorithm is described as the computation of a stable matching in an auxiliary instance, in which each contract is replaced with three of its copies and all agents have strict preferences on the copied contracts. The construction of this auxiliary instance is symmetric for the two sides, which facilitates a simple symmetric analysis. We use the notion of matroid-kernel for computation in the auxiliary instance and exploit the base-orderability of laminar matroids to show the approximation ratio.
In a special case in which each worker is assigned at most one contract and each firm has a strict preference, our algorithm defines a 3/2-approximation mechanism that is strategy-proof for workers.
Stable matching
Approximation algorithm
Matroid
Strategy-proofness
Theory of computation~Approximation algorithms analysis
Theory of computation~Algorithmic game theory
71:1-71:16
Regular Paper
This work was supported by JSPS KAKENHI Grant Number JP18K18004, JST PRESTO Grant Number JPMJPR212B, and the joint project of Kyoto University and Toyota Motor Corporation, titled "Advanced Mathematical Science for Mobility Society".
https://arxiv.org/abs/2107.03076
The author thanks the anonymous reviewers for their helpful comments.
Yu
Yokoi
Yu Yokoi
National Institute of Informatics, Hitotsubashi, Chiyoda-ku, Tokyo, Japan
https://orcid.org/0000-0002-7316-5434
10.4230/LIPIcs.ISAAC.2021.71
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Y. Yokoi. An approximation algorithm for maximum stable matching with ties and constraints. arXiv preprint, 2021. URL: http://arxiv.org/abs/2107.03076.
http://arxiv.org/abs/2107.03076
Yu Yokoi
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