{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/diverse-weighted-bipartite-b-matching","title":"Diverse Weighted Bipartite b-Matching","arxiv_id":"1702.07134","date":"2017-02-23","proceeding":null,"authors":["Faez Ahmed","John P. Dickerson","Mark Fuge"],"abstract":"Bipartite matching, where agents on one side of a market are matched to\nagents or items on the other, is a classical problem in computer science and\neconomics, with widespread application in healthcare, education, advertising,\nand general resource allocation. A practitioner's goal is typically to maximize\na matching market's economic efficiency, possibly subject to some fairness\nrequirements that promote equal access to resources. A natural balancing act\nexists between fairness and efficiency in matching markets, and has been the\nsubject of much research.\n  In this paper, we study a complementary goal---balancing diversity and\nefficiency---in a generalization of bipartite matching where agents on one side\nof the market can be matched to sets of agents on the other. Adapting a\nclassical definition of the diversity of a set, we propose a quadratic\nprogramming-based approach to solving a supermodular minimization problem that\nbalances diversity and total weight of the solution. We also provide a scalable\ngreedy algorithm with theoretical performance bounds. We then define the price\nof diversity, a measure of the efficiency loss due to enforcing diversity, and\ngive a worst-case theoretical bound. Finally, we demonstrate the efficacy of\nour methods on three real-world datasets, and show that the price of diversity\nis not bad in practice.","url_abs":"http://arxiv.org/abs/1702.07134v2","url_pdf":"http://arxiv.org/pdf/1702.07134v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"diverse-weighted-bipartite-b-matching","repo_url":"https://github.com/faezahmed/diverse_matching","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"diversity","task_name":"Diversity"},{"task_slug":"fairness","task_name":"Fairness"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1702.07134","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1702.07134"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/faezahmed/diverse_matching","reach":null}],"summary":{"ran_draft_wrong":1,"unverified":1},"by_repo_kind":{"official":{"samples":2,"ran":1,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":2,"samples":[{"code_sha256_prefix":"e0693015cdd89cfc","entry":"find_graph_weighted_gender","repo":"faezahmed/diverse_matching","repo_kind":"official","path":"graph_alg_country_gender_final.py","file_url":"https://github.com/faezahmed/diverse_matching/blob/HEAD/graph_alg_country_gender_final.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"MISDECLARED","metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"e0693015cdd89cfc"}},{"code_sha256_prefix":"8675e3d8c5d84be9","entry":"transfer_multiple_worker","repo":"faezahmed/diverse_matching","repo_kind":"official","path":"graph_alg_country_gender_final.py","file_url":"https://github.com/faezahmed/diverse_matching/blob/HEAD/graph_alg_country_gender_final.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"8675e3d8c5d84be9"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}