{"ID":2882932,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.10129","arxiv_id":"2508.10129","title":"FPT-Approximability of Stable Matching Problems","abstract":"We study parameterized approximability of three optimization problems related to stable matching: (1) Min-BP-SMI: Given a stable marriage instance and a number k, find a size-at-least-k matching that minimizes the number $β$ of blocking pairs; (2) Min-BP-SRI: Given a stable roommates instance, find a matching that minimizes the number $β$ of blocking pairs; (3) Max-SMTI: Given a stable marriage instance with preferences containing ties, find a maximum-size stable matching. The first two problems are known to be NP-hard to approximate to any constant factor and W[1]-hard with respect to $β$, making the existence of an EPTAS or FPT-algorithms unlikely. We show that they are W[1]-hard with respect to $β$ to approximate to any function of $β$. This means that unless FPT=W[1], there is no FPT-approximation scheme for the parameter $β$. The last problem (Max-SMTI) is known to be NP-hard to approximate to factor-29/33 and W[1]-hard with respect to the number of ties. We complement this and present an FPT-approximation scheme for the parameter \"number of agents with ties\".","short_abstract":"We study parameterized approximability of three optimization problems related to stable matching: (1) Min-BP-SMI: Given a stable marriage instance and a number k, find a size-at-least-k matching that minimizes the number $β$ of blocking pairs; (2) Min-BP-SRI: Given a stable roommates instance, find a matching that mini...","url_abs":"https://arxiv.org/abs/2508.10129","url_pdf":"https://arxiv.org/pdf/2508.10129v1","authors":"[\"Jiehua Chen\",\"Sanjukta Roy\",\"Sofia Simola\"]","published":"2025-08-13T18:48:43Z","proceeding":"cs.GT","tasks":"[\"cs.GT\",\"cs.MA\"]","methods":"[]","has_code":false}