{"type":"ScholarlyArticle","title":"An Algorithm for Multi-Attribute Diverse Matching","authors":[{"name":"Saba Ahmadi","slug":"saba-ahmadi","given":"Saba","family":"Ahmadi","affiliation":"Department of Computer Science , University of Maryland"},{"name":"Faez Ahmed","slug":"faez-ahmed","given":"Faez","family":"Ahmed","affiliation":"Department of Mechanical Engineering , Northwestern University"},{"name":"John P. Dickerson","slug":"john-p-dickerson","given":"John P.","family":"Dickerson","affiliation":"Department of Computer Science , University of Maryland"},{"name":"Mark Fuge","slug":"mark-fuge","given":"Mark","family":"Fuge","affiliation":"Department of Mechanical Engineering , University of Maryland"},{"name":"Samir Khuller","slug":"samir-khuller","given":"Samir","family":"Khuller","affiliation":"Department of Computer Science , Northwestern University"}],"abstract":"Bipartite b-matching, where agents on one side of a market are matched to one or more agents or items on the other, is a classical model that is used in myriad application areas such as healthcare, advertising, education, and general resource allocation. Traditionally, the primary goal of such models is to maximize a linear function of the constituent matches (e.g., linear social welfare maximization) subject to some constraints. Recent work has studied a new goal of balancing whole-match diversity and economic efficiency, where the objective is instead a monotone submodular function over the matching.  Basic versions of this problem are solvable in polynomial time. In this work, we prove that the problem of simultaneously maximizing diversity along several features (e.g., country of citizenship, gender, skills) is NP-hard. To address this problem, we develop the first combinatorial algorithm that constructs provably-optimal diverse b-matchings in pseudo-polynomial time. We also provide a Mixed-Integer Quadratic formulation for the same problem and show that our method guarantees optimal solutions and takes less computation time for a reviewer assignment application. The source code is made available at https://github.com/faezahmed/diverse_matching.","doi":"10.24963/ijcai.2020/1","url":"https://ijcai.org/proceedings/2020/1","pdf":"https://ijcai.org/proceedings/2020/0001.pdf","markdown":"https://ijcai.org/proceedings/2020/1.md","bibtex":"https://ijcai.org/proceedings/2020/bibtex/1","volume":{"slug":"2020","title":"Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2020","url":"https://ijcai.org/proceedings/2020/","year":2020,"location":"Yokohama","dates":"January 2021 (postponed from 11-17 July 2020)","editors":"Christian Bessiere","isbn":"978-0-9992411-6-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2020"},"section":"Agent-based and Multi-agent Systems","track":"Main track","number":1,"pages":{"first":3,"last":9},"keywords":["Heuristic Search and Game Playing: Combinatorial Search and Optimisation","Humans and AI: Human Computation and Crowdsourcing","Agent-based and Multi-agent Systems: Economic Paradigms, Auctions and Market-Based Systems"],"videos":[{"label":"Video","url":"https://videos.ijcai20.org/25227/file_25227.m3u8","length_sec":275,"provider":"hls"}],"references":[{"position":1,"raw":"[Agrawal et al., 2018] Shipra Agrawal, Morteza Zadimoghaddam, and Vahab Mirrokni. Proportional allocation: Simple, dis- tributed, and diverse matching with high entropy. In International Conference on Machine Learning (ICML), pages 99-108, 2018.","title":"Proportional allocation: Simple, distributed, and diverse matching with high entropy","authors":"Shipra Agrawal, Morteza Zadimoghaddam, Vahab Mirrokni","year":"2018","venue":"International Conference on Machine Learning (ICML)","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Ahmed and Fuge, 2018] Faez Ahmed and Mark Fuge. Ranking ideas for diversity and quality. Journal of Mechanical Design, 140(1):011101, 2018.","title":"Ranking ideas for diversity and quality","authors":"Ahmed, Fuge ;, Faez Ahmed, Mark Fuge","year":"2018","venue":"Journal of Mechanical Design","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Ahmed et al., 2017] Faez Ahmed, John P. Dickerson, and Mark Fuge. Diverse weighted bipartite b-matching. In Proceedings of the 26th International Joint Conference on Artificial Intelligence, IJCAI'17, pages 35-41. AAAI Press, 2017.","title":"Diverse weighted bipartite b-matching","authors":"Faez Ahmed, John P Dickerson, Mark Fuge","year":"2017","venue":"Proceedings of the 26th International Joint Conference on Artificial Intelligence, IJCAI'17","doi":null,"url":null,"internal_url":"/proceedings/2017/6"},{"position":4,"raw":"[Basu Roy et al., 2015] Senjuti Basu Roy, Ioanna Lykourentzou, Saravanan Thirumuruganathan, Sihem Amer-Yahia, and Gau- tam Das. Task assignment optimization in knowledge-intensive crowdsourcing. The VLDB Journal-The International Journal on Very Large Data Bases, 24(4):467-491, 2015.","title":"Senjuti Basu Roy, Ioanna Lykourentzou, Saravanan Thirumuruganathan, Sihem Amer-Yahia, and Gautam Das","authors":"Roy Basu","year":"2015","venue":"The VLDB Journal-The International Journal on Very Large Data Bases","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Benabbou et al., 2018] Nawal Benabbou, Mithun Chakraborty, Xuan-Vinh Ho, Jakub Sliwinski, and Yair Zick. Diversity con- straints in public housing allocation. In Proceedings of the 17th International Conference on Autonomous Agents and MultiA- gent Systems, pages 973-981. International Foundation for Au- tonomous Agents and Multiagent Systems, 2018.","title":"Diversity constraints in public housing allocation","authors":"Nawal Benabbou, Mithun Chakraborty, Xuan-Vinh Ho, Jakub Sliwinski, Yair Zick","year":"2018","venue":"Proceedings of the 17th International Conference on Autonomous Agents and MultiAgent Systems","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Bertsimas et al., 2019] Dimitris Bertsimas, Theodore Papalex- opoulos, Nikolaos Trichakis, Yuchen Wang, Ryutaro Hirose, and Parsia A Vagefi. Balancing efficiency and fairness in liver trans- plant access: tradeoff curves for the assessment of organ distri- bution policies. Transplantation, 2019.","title":"Balancing efficiency and fairness in liver transplant access: tradeoff curves for the assessment of organ distribution policies","authors":"Dimitris Bertsimas, Theodore Papalexopoulos, Nikolaos Trichakis, Yuchen Wang, Ryutaro Hirose, Parsia A Vagefi","year":"2019","venue":"Transplantation","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Carbonell and Goldstein, 1998] Jaime Carbonell and Jade Gold- stein. The use of MMR, diversity-based reranking for reordering documents and producing summaries. In Proceedings of the 21st Annual International ACM SIGIR Conference on Research and Development in Information Retrieval, pages 335-336. ACM, 1998.","title":"Jaime Carbonell and Jade Goldstein. The use of MMR, diversity-based reranking for reordering documents and producing summaries","authors":"Goldstein Carbonell","year":"1998","venue":"Proceedings of the 21st Annual International ACM SIGIR Conference on Research and Development in Information Retrieval","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Charlin and Zemel, 2013] Laurent Charlin and Richard Zemel. The toronto paper matching system: an automated paper- reviewer assignment system. 2013.","title":"The toronto paper matching system: an automated paperreviewer assignment system","authors":"Zemel Charlin, Laurent Charlin, Richard Zemel","year":"2013","venue":null,"doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Cherkassky et al., 1993] Boris Cherkassky, Andrew V. Goldberg, and Tomasz Radzik. Shortest paths algorithms: Theory and ex- perimental evaluation. Mathematical Programming, 73:129-174, 1993.","title":"Shortest paths algorithms: Theory and experimental evaluation","authors":"Boris Cherkassky, Andrew V Goldberg, Tomasz Radzik","year":"1993","venue":"Mathematical Programming","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Dickerson and Sandholm, 2015] John P. Dickerson and Tuomas Sandholm. Futurematch: Combining human value judgments and machine learning to match in dynamic environments. In Pro- ceedings of the Twenty-Ninth AAAI Conference on Artificial In- telligence, AAAI'15, pages 622-628. AAAI Press, 2015.","title":"Futurematch: Combining human value judgments and machine learning to match in dynamic environments","authors":"John P Dickerson, Tuomas Sandholm","year":"2015","venue":"Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence, AAAI'15","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Dickerson et al., 2019] John P. Dickerson, Karthik Abinav Sankararaman, Aravind Srinivasan, and Pan Xu. Balancing relevance and diversity in online bipartite matching via submod- ularity. In AAAI Conference on Artificial Intelligence (AAAI), 2019.","title":"Balancing relevance and diversity in online bipartite matching via submodularity","authors":"John P Dickerson, Karthik Abinav Sankararaman, Aravind Srinivasan, Pan Xu","year":"2019","venue":"AAAI Conference on Artificial Intelligence (AAAI)","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Drummond et al., 2015] Joanna Drummond, Andrew Perrault, and Fahiem Bacchus. Sat is an effective and complete method for solving stable matching problems with couples. In IJCAI, pages 518-525, 2015.","title":"Sat is an effective and complete method for solving stable matching problems with couples","authors":"Joanna Drummond, Andrew Perrault, Fahiem Bacchus","year":"2015","venue":"IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2015/79"},{"position":13,"raw":"[Goldberg and Radzik, 1993] Andrew V. Goldberg and Tomasz Radzik. A heuristic improvement of the bellman-ford algorithm, 1993. [Gölz and Procaccia, 2019] Paul Gölz and Ariel D Procaccia. Mi- gration as submodular optimization. In AAAI Conference on Ar- tificial Intelligence (AAAI), 2019.","title":"A heuristic improvement of the bellman-ford algorithm","authors":"Andrew V Goldberg, Tomasz Radzik, Paul Gölz, Ariel D Procaccia","year":"1993","venue":"AAAI Conference on Artificial Intelligence (AAAI)","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Grgić-Hlača et al., 2018] Nina Grgić-Hlača, Muhammad Bilal Za- far, Krishna P Gummadi, and Adrian Weller. Beyond distribu- tive fairness in algorithmic decision making: Feature selection for procedurally fair learning. In AAAI Conference on Artificial Intelligence (AAAI), 2018.","title":"Beyond distributive fairness in algorithmic decision making: Feature selection for procedurally fair learning","authors":"Nina Grgić-Hlača, Muhammad Bilal Zafar, Krishna P Gummadi, Adrian Weller","year":"2018","venue":"AAAI Conference on Artificial Intelligence (AAAI)","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Hirschman, 1964] Albert O Hirschman. The paternity of an index. The American economic review, 54(5):761-762, 1964.","title":"The paternity of an index","authors":"Albert O Hirschman","year":"1964","venue":"The American economic review","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Hunt et al., 2015] Vivian Hunt, Dennis Layton, and Sara Prince. Diversity matters. McKinsey & Company, 1:15-29, 2015.","title":"Diversity matters","authors":"Vivian Hunt, Dennis Layton, Sara Prince","year":"2015","venue":"McKinsey & Company","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Karimzadehgan and Zhai, 2009] Maryam Karimzadehgan and ChengXiang Zhai. Constrained multi-aspect expertise matching for committee review assignment. In ACM Conference on Infor- mation and Knowledge Management (CIKM), pages 1697-1700, 2009.","title":"Maryam Karimzadehgan and ChengXiang Zhai. Constrained multi-aspect expertise matching for committee review assignment","authors":"Zhai Karimzadehgan","year":"2009","venue":"ACM Conference on Information and Knowledge Management (CIKM)","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Kobren et al., 2019] Ari Kobren, Barna Saha, and Andrew McCal- lum. Paper matching with local fairness constraints. In Pro- ceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, KDD '19, pages 1247- 1257, New York, NY, USA, 2019. ACM.","title":"Paper matching with local fairness constraints","authors":"Ari Kobren, Barna Saha, Andrew Mccallum","year":"2019","venue":"Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, KDD '19","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Kulesza et al., 2012] Alex Kulesza, Ben Taskar, et al. Determi- nantal point processes for machine learning. Foundations and Trends R in Machine Learning, 5(2-3):123-286, 2012.","title":"Determinantal point processes for machine learning","authors":"Alex Kulesza, Ben Taskar","year":"2012","venue":"Foundations and Trends R in Machine Learning","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Kurata et al., 2017] Ryoji Kurata, Naoto Hamada, Atsushi Iwasaki, and Makoto Yokoo. Controlled school choice with soft bounds and overlapping types. Journal of Artificial Intelligence Research, 58:153-184, 2017.","title":"Controlled school choice with soft bounds and overlapping types","authors":"Ryoji Kurata, Naoto Hamada, Atsushi Iwasaki, Makoto Yokoo","year":"2017","venue":"Journal of Artificial Intelligence Research","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Lian et al., 2018] Jing Wu Lian, Nicholas Mattei, Renee Noble, and Toby Walsh. The conference paper assignment problem: Using order weighted averages to assign indivisible goods. In Thirty-Second AAAI Conference on Artificial Intelligence, 2018.","title":"The conference paper assignment problem: Using order weighted averages to assign indivisible goods","authors":"Jing Wu, Lian, Nicholas Mattei, Renee Noble, Toby Walsh","year":"2018","venue":"Thirty-Second AAAI Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Lin and Bilmes, 2012] Hui Lin and Jeff A Bilmes. Learning mix- tures of submodular shells with application to document summa- rization. arXiv preprint arXiv:1210.4871, 2012.","title":"Learning mixtures of submodular shells with application to document summarization","authors":"Hui Lin, Jeff A Bilmes","year":"2012","venue":null,"doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Liu et al., 2014] Xiang Liu, Torsten Suel, and Nasir Memon. A robust model for paper reviewer assignment. In Proceedings of the 8th ACM Conference on Recommender Systems, RecSys '14, pages 25-32, New York, NY, USA, 2014. ACM.","title":"A robust model for paper reviewer assignment","authors":"Xiang Liu, Torsten Suel, Nasir Memon","year":"2014","venue":"Proceedings of the 8th ACM Conference on Recommender Systems, RecSys '14","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Minoux, 1986] M. Minoux. Solving integer minimum cost flows with separable convex cost objective polynomially, pages 237- 239. Springer Berlin Heidelberg, Berlin, Heidelberg, 1986.","title":"Solving integer minimum cost flows with separable convex cost objective polynomially","authors":"M Minoux","year":"1986","venue":null,"doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Østergaard et al., 2011] Christian R Østergaard, Bram Timmer- mans, and Kari Kristinsson. Does a different view create some- thing new? the effect of employee diversity on innovation. Re- search Policy, 40(3):500-509, 2011.","title":"Does a different view create something new? the effect of employee diversity on innovation","authors":"Østergaard","year":"2011","venue":"Research Policy","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Ross et al., 2010] Joel Ross, Lilly Irani, M Silberman, Andrew Zaldivar, and Bill Tomlinson. Who are the crowdworkers?: shift- ing demographics in mechanical turk. In CHI'10 extended ab- stracts on Human factors in computing systems, pages 2863- 2872. ACM, 2010.","title":"Who are the crowdworkers?: shifting demographics in mechanical turk","authors":"Joel Ross, Lilly Irani, M Silberman, Andrew Zaldivar, Bill Tomlinson","year":"2010","venue":"CHI'10 extended abstracts on Human factors in computing systems","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Schumann et al., 2019] Candice Schumann, Samsara N. Counts, Jeffrey Foster, and John P. Dickerson. The diverse cohort se- lection problem. In International Conference on Autonomous Agents and Multi-Agent Systems (AAMAS), 2019.","title":"The diverse cohort selection problem","authors":"Candice Schumann, N Samsara, Jeffrey Counts, John P Foster, Dickerson","year":"2019","venue":"International Conference on Autonomous Agents and Multi-Agent Systems (AAMAS)","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}