A CP-Based Approach for Popular Matching
نویسندگان
چکیده
Description • One integer variable xi per applicant ai . • Domain of xi is D(xi) = {j |(ai, pj) ∈ E} ∪ {li}. For each applicant ai , we denote by: • f (ai) the best post in its preference list, called f -post. • li the last-resort post / ∈ P for ai , called l -post. A post pj ∈ P is called an f -post if ∃ai ∈ A such that f (ai) = pj . Preferences without ties For each applicant ai , we denote by s(ai) the best choice for ai that is not an f -post, called s-post. Lemma [Abraham et al.] A matching M is popular iff the following conditions hold: • Every f -post is matched, and • For each applicant ai , M(ai) ∈ {f (ai), s(ai)}.
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