Quasi-Popular Matchings, Optimality, and Extended Formulations
نویسندگان
چکیده
Let [Formula: see text] be an instance of the stable marriage problem in which every vertex ranks its neighbors a strict order preference. A matching is popular if does not lose head-to-head election against any matching. Popular matchings generalize matchings. Unfortunately, when there are edge costs, to find or even approximate up factor minimum cost NP-hard. min-cost Our goal efficiently compute at most by paying price mildly relaxing popularity. main positive results two bicriteria algorithms that polynomial time “quasi-popular” text]. Moreover, one finds quasi-popular fractional matching, could much smaller than Key other algorithm polynomial-size extended formulation for integral polytope sandwiched between and polytopes. We complement these showing it NP-hard both polytopes have near-exponential extension complexity.
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ژورنال
عنوان ژورنال: Mathematics of Operations Research
سال: 2022
ISSN: ['0364-765X', '1526-5471']
DOI: https://doi.org/10.1287/moor.2021.1139