Reproduce “Envy-free Matchings with Lower Quotas” on OpenResearch
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About this paper
Yu Yokoi
This paper investigates the existence and computational complexity of envy-free matchings in settings with lower quotas, including the Hospitals/Residents problem (HR-LQ) and the more general Classified Stable Matching (CSM) model. It provides efficient algorithms for HR-LQ and CSM with paramodular quotas, while demonstrating NP-hardness for general CSM instances.
Key insights
- Envy-freeness for HR-LQ can be characterized by whether all hospitals are fully subscribed in a stable matching of an auxiliary instance where upper quotas are set to original lower quotas.
- Deciding the existence of an envy-free matching in the general Classified Stable Matching (CSM) model is NP-hard, indicating inherent computational difficulty for arbitrary quota functions.
- CSM instances with paramodular quota functions, which are linked to generalized matroids, offer a tractable special case, allowing for efficient determination of envy-free matching existence.
Summary by alphaXiv.
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