{"type":"ScholarlyArticle","title":"Online Roommate Allocation Problem","authors":[{"name":"Guangda Huzhang","slug":"guangda-huzhang","given":"Guangda","family":"Huzhang","affiliation":""},{"name":"Xin Huang","slug":"xin-huang","given":"Xin","family":"Huang","affiliation":""},{"name":"Shengyu Zhang","slug":"shengyu-zhang","given":"Shengyu","family":"Zhang","affiliation":"Department of Computer Science and Engineering , The Chinese University of Hong Kong"},{"name":"Xiaohui Bei","slug":"xiaohui-bei","given":"Xiaohui","family":"Bei","affiliation":"School of Physical and Mathematical Sciences , Nanyang Technological University 2 ,"}],"abstract":"We study the online allocation problem under a roommate market model introduced in [Chan et al., 2016]. Consider a fixed supply of n rooms and a list of 2n applicants arriving sequentially in an online fashion. The problem is to assign a room to each person upon her arrival, such that after the algorithm terminates, each room is shared by exactly two people. We focus on two objectives: (1) maximizing the social welfare, which is defined as the sum of valuations that applicants have for their rooms, plus the happiness value between each pair of roommates; (2) the allocation should satisfy certain stability conditions, such that no group of people would be willing to switch roommates or rooms. We first show a polynomial-time online algorithm that achieves constant competitive ratio for social welfare maximization. We then extend it to the case where each room is assigned to c > 2 people, and achieve a competitive ratio of Ω(1/c^2). Finally, we show both positive and negative results in satisfying different stability conditions in this online setting.","doi":"10.24963/ijcai.2017/34","url":"https://ijcai.org/proceedings/2017/34","pdf":"https://ijcai.org/proceedings/2017/0034.pdf","markdown":"https://ijcai.org/proceedings/2017/34.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/34","volume":{"slug":"2017","title":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2017","url":"https://ijcai.org/proceedings/2017/","year":2017,"location":"Melbourne, Australia","dates":"19-25 August 2017","editors":"Carles Sierra","isbn":"978-0-9992411-0-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2017"},"section":"Agent-based and Multi-agent Systems","track":"Main track","number":34,"pages":{"first":235,"last":241},"keywords":["Agent-based and Multi-agent Systems: Social Choice Theory","Planning and Scheduling: Planning under Uncertainty","Agent-based and Multi-agent Systems: Multi-agent Planning"],"videos":[],"references":[{"position":1,"raw":"[Aggarwal et al., 2011] Gagan Aggarwal, Gagan Goel, Chinmay Karande, and Aranyak Mehta. Online vertex- weighted bipartite matching and single-bid budgeted allocations. In Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms, pages 1253-1264. SIAM, 2011.","title":"Online vertexweighted bipartite matching and single-bid budgeted allocations","authors":"Gagan Aggarwal, Gagan Goel, Chinmay Karande, Aranyak Mehta","year":"2011","venue":"Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Babaioff et al., 2007] Moshe Babaioff, Nicole Immorlica, and Robert Kleinberg. Matroids, secretary problems, and online mechanisms. In Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms, pages 434-443. Society for Industrial and Applied Mathe- matics, 2007.","title":"Moshe Babaioff, Nicole Immorlica, and Robert Kleinberg. Matroids, secretary problems, and online mechanisms","authors":"Babaioff","year":"2007","venue":"Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Biró et al., 2010] Péter Biró, Robert W Irving, and David F Manlove. Popular matchings in the marriage and room- mates problems. In Algorithms and Complexity, pages 97- 108. Springer, 2010.","title":"Popular matchings in the marriage and roommates problems","authors":"Péter Biró, Robert W Irving, David F Manlove","year":"2010","venue":"Algorithms and Complexity","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Cechlárová and Manlove, 2005] Katarína Cechlárová and David F Manlove. The exchange-stable marriage problem. Discrete Applied Mathematics, 152(1):109-122, 2005.","title":"The exchange-stable marriage problem","authors":"Manlove Cechlárová, Katarína Cechlárová, David F Manlove","year":"2005","venue":"Discrete Applied Mathematics","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Chan et al., 2016] Pak Hay Chan, Xin Huang, Zhengyang Liu, Chihao Zhang, and Shengyu Zhang. Assignment and pricing in roommate market. In Thirtieth AAAI Conference on Artificial Intelligence, pages 446-452, 2016.","title":"Assignment and pricing in roommate market","authors":"Pak Hay, Chan, Xin Huang, Zhengyang Liu, Chihao Zhang, Shengyu Zhang","year":"2016","venue":"Thirtieth AAAI Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Dimitrov and Plaxton, 2008] Nedialko B Dimitrov and C Greg Plaxton. Competitive weighted matching in transversal matroids. In International Colloquium on Au- tomata, Languages, and Programming, pages 397-408. Springer, 2008.","title":"Competitive weighted matching in transversal matroids","authors":"Plaxton ; Dimitrov, B Nedialko, C Dimitrov, Greg Plaxton","year":"2008","venue":"International Colloquium on Automata, Languages, and Programming","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Eriksson et al., 2006] Kimmo Eriksson, Jonas Sjöstrand, and Pontus Strimling. Three-dimensional stable match- ing with cyclic preferences. Mathematical Social Sciences, 52(1):77-87, 2006.","title":"Three-dimensional stable matching with cyclic preferences","authors":"Eriksson","year":"2006","venue":"Mathematical Social Sciences","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Ferguson, 1989] Thomas S Ferguson. Who solved the sec- retary problem? Statistical science, pages 282-289, 1989.","title":"Who solved the secretary problem? Statistical science","authors":"Thomas S Ferguson","year":"1989","venue":null,"doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Gale and Shapley, 1962] David Gale and Lloyd S Shapley. College admissions and the stability of marriage. Ameri- can mathematical monthly, pages 9-15, 1962.","title":"College admissions and the stability of marriage","authors":"Shapley ; Gale, David Gale, Lloyd S Shapley","year":"1962","venue":"American mathematical monthly","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Gharan and Vondrák, 2013] Shayan Oveis Gharan and Jan Vondrák. On variants of the matroid secretary problem. Algorithmica, 67(4):472-497, 2013.","title":"On variants of the matroid secretary problem","authors":"Shayan Oveis, Gharan, Jan Vondrák","year":"2013","venue":"Algorithmica","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Hajiaghayi et al., 2007] Mohammad Taghi Hajiaghayi, Robert Kleinberg, and Tuomas Sandholm. Automated online mechanism design and prophet inequalities. In Thirty-Frist AAAI Conference on Artificial Intelligence, volume 7, pages 58-65, 2007.","title":"Automated online mechanism design and prophet inequalities","authors":"Mohammad Taghi, Hajiaghayi, Robert Kleinberg, Tuomas Sandholm","year":"2007","venue":"Thirty-Frist AAAI Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Huang, 2007] Chien-Chung Huang. Two's company, three'sa crowd: Stable family and threesome roommates problems. In Algorithms-ESA 2007, pages 558-569.","title":"Two's company, three'sa crowd: Stable family and threesome roommates problems","authors":"Chien-Chung Huang","year":null,"venue":"Algorithms-ESA 2007","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Im and Wang, 2011] Sungjin Im and Yajun Wang. Secretary problems: Laminar matroid and interval scheduling. In Proceedings of the twenty-second annual ACM-SIAM sym- posium on Discrete Algorithms, pages 1265-1274. SIAM, 2011.","title":"Secretary problems: Laminar matroid and interval scheduling","authors":"Wang ; ] Sungjin Im, Yajun Im, Wang","year":"2011","venue":"Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Irving and Manlove, 2002] Robert W Irving and David F Manlove. The stable roommates problem with ties. Jour- nal of Algorithms, 43(1):85-105, 2002.","title":"The stable roommates problem with ties","authors":"W Robert, David F Irving, Manlove","year":"2002","venue":"Journal of Algorithms","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Irving, 1985] Robert W Irving. An efficient algorithm for the \"stable roommates\" problem. Journal of Algorithms, 6(4):577-595, 1985.","title":"An efficient algorithm for the \"stable roommates\" problem","authors":"Irving Robert","year":"1985","venue":"Journal of Algorithms","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Iwama and Miyazaki, 2008] Kazuo Iwama and Shuichi Miyazaki. A survey of the stable marriage problem and its variants. In Informatics Education and Research for Knowledge-Circulating Society, 2008. ICKS 2008. Inter- national Conference on, pages 131-136. IEEE, 2008.","title":"A survey of the stable marriage problem and its variants","authors":"Kazuo Iwama, Shuichi Miyazaki","year":"2008","venue":"Informatics Education and Research for Knowledge-Circulating Society","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Kalyanasundaram and Pruhs, 1993] Bala Kalyanasundaram and Kirk Pruhs. Online weighted matching. Journal of Algorithms, 14(3):478-488, 1993.","title":"Online weighted matching","authors":"Pruhs Kalyanasundaram, Bala Kalyanasundaram, Kirk Pruhs","year":"1993","venue":"Journal of Algorithms","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Karp et al., 1990] Richard M Karp, Umesh V Vazirani, and Vijay V Vazirani. An optimal algorithm for on-line bipar- tite matching. In Proceedings of the twenty-second annual ACM symposium on Theory of computing, pages 352-358. ACM, 1990.","title":"An optimal algorithm for on-line bipartite matching","authors":"Umesh V Richard M Karp, Vijay V Vazirani, Vazirani","year":"1990","venue":"Proceedings of the twenty-second annual ACM symposium on Theory of computing","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Kesselheim et al., 2013] Thomas Kesselheim, Klaus Radke, Andreas Tönnis, and Berthold Vöcking. An optimal online algorithm for weighted bipartite matching and extensions to combinatorial auctions. In Algorithms-ESA 2013, pages 589-600. Springer, 2013.","title":"An optimal online algorithm for weighted bipartite matching and extensions to combinatorial auctions","authors":"Thomas Kesselheim, Klaus Radke, Andreas Tönnis, Berthold Vöcking","year":"2013","venue":"Algorithms-ESA 2013","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Kesselheim et al., 2014] Thomas Kesselheim, Andreas Tönnis, Klaus Radke, and Berthold Vöcking. Primal beats dual on online packing lps in the random-order model. In Proceedings of the 46th Annual ACM Symposium on Theory of Computing, pages 303-312. ACM, 2014.","title":"Primal beats dual on online packing lps in the random-order model","authors":"Thomas Kesselheim, Andreas Tönnis, Klaus Radke, Berthold Vöcking","year":"2014","venue":"Proceedings of the 46th Annual ACM Symposium on Theory of Computing","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Knuth, 1997] Donald Ervin Knuth. Stable marriage and its relation to other combinatorial problems: An introduction to the mathematical analysis of algorithms, volume 10. American Mathematical Soc., 1997.","title":"Stable marriage and its relation to other combinatorial problems: An introduction to the mathematical analysis of algorithms","authors":"Donald Ervin, Knuth","year":"1997","venue":null,"doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Ng and Hirschberg, 1991] Cheng Ng and Daniel S Hirschberg. Three-dimensional stable matching problems. SIAM Journal on Discrete Mathematics, 4(2):245-252, 1991.","title":"Three-dimensional stable matching problems","authors":"Cheng Ng, Daniel S Hirschberg","year":"1991","venue":"SIAM Journal on Discrete Mathematics","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Soto, 2013] José A Soto. Matroid secretary problem in the random-assignment model. SIAM Journal on Computing, 42(1):178-211, 2013.","title":"Matroid secretary problem in the random-assignment model","authors":"A José, Soto","year":"2013","venue":"SIAM Journal on Computing","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}