{"type":"ScholarlyArticle","title":"Welfare Loss in Connected Resource Allocation","authors":[{"name":"Xiaohui Bei","slug":"xiaohui-bei","given":"Xiaohui","family":"Bei","affiliation":"Nanyang Technological University"},{"name":"Alexander Lam","slug":"alexander-lam","given":"Alexander","family":"Lam","affiliation":"City University of Hong Kong"},{"name":"Xinhang Lu","slug":"xinhang-lu","given":"Xinhang","family":"Lu","affiliation":"UNSW Sydney"},{"name":"Warut Suksompong","slug":"warut-suksompong","given":"Warut","family":"Suksompong","affiliation":"National University of Singapore"}],"abstract":"We study the allocation of indivisible goods that form an undirected graph and investigate the worst-case welfare loss when requiring that each agent must receive a connected subgraph. Our focus is on both egalitarian and utilitarian welfare. Specifically, we introduce the concept of egalitarian (resp., utilitarian) price of connectivity, which captures the worst-case ratio between the optimal egalitarian (resp., utilitarian) welfare among all allocations and that among the connected allocations. We provide tight or asymptotically tight bounds on the price of connectivity for various large classes of graphs when there are two agents, and for paths, stars and cycles in the general case. Many of our results are supplemented with algorithms which find connected allocations with a welfare guarantee corresponding to the price of connectivity.","doi":"10.24963/ijcai.2024/294","url":"https://ijcai.org/proceedings/2024/294","pdf":"https://ijcai.org/proceedings/2024/0294.pdf","markdown":"https://ijcai.org/proceedings/2024/294.md","bibtex":"https://ijcai.org/proceedings/2024/bibtex/294","volume":{"slug":"2024","title":"Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2024","url":"https://ijcai.org/proceedings/2024/","year":2024,"location":"Jeju, Korea","dates":"3-9 August 2024","editors":"Kate Larson","isbn":"978-1-956792-04-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2024"},"section":"Game Theory and Economic Paradigms","track":"Main Track","number":294,"pages":{"first":2660,"last":2668},"keywords":["Agent-based and Multi-agent Systems: MAS: Resource allocation","Game Theory and Economic Paradigms: GTEP: Fair division"],"videos":[],"references":[{"position":1,"raw":"[Amanatidis et al., 2023] Georgios Amanatidis, Haris Aziz, Georgios Birmpas, Aris Filos-Ratsikas, Bo Li, Hervé Moulin, Alexandros A. Voudouris, and Xiaowei Wu. Fair division of indivisible goods: Recent progress and open questions. Artificial Intelligence, 322:103965, 2023.","title":"Fair division of indivisible goods: Recent progress and open questions","authors":"Georgios Amanatidis, Haris Aziz, Georgios Birmpas, Aris Filos-Ratsikas, Bo Li, Hervé Moulin, Alexandros A Voudouris, Xiaowei Wu","year":"2023","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Asadpour and Saberi, 2010] Arash Asadpour and Amin Saberi. An approximation algorithm for max-min fair allo- cation of indivisible goods. SIAM Journal on Computing, 39(7):2970-2989, 2010.","title":"Arash Asadpour and Amin Saberi. An approximation algorithm for max-min fair allocation of indivisible goods","authors":"Saberi Asadpour","year":"2010","venue":"SIAM Journal on Computing","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Barman et al., 2020] Siddharth Barman, Umang Bhaskar, and Nisarg Shah. Optimal bounds on the price of fair- ness for indivisible goods. In Proceedings of the 16th International Conference on Web and Internet Economics (WINE), pages 356-369, 2020.","title":"Optimal bounds on the price of fairness for indivisible goods","authors":"Siddharth Barman, Umang Bhaskar, Nisarg Shah","year":"2020","venue":"Proceedings of the 16th International Conference on Web and Internet Economics (WINE)","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Bei et al., 2021] Xiaohui Bei, Xinhang Lu, Pasin Manu- rangsi, and Warut Suksompong. The price of fairness for indivisible goods. Theory of Computing Systems, 65(7):1069-1093, 2021.","title":"The price of fairness for indivisible goods","authors":"Xiaohui Bei, Xinhang Lu, Pasin Manurangsi, Warut Suksompong","year":"2021","venue":"Theory of Computing Systems","doi":null,"url":null,"internal_url":"/proceedings/2019/12"},{"position":5,"raw":"[Bei et al., 2022] Xiaohui Bei, Ayumi Igarashi, Xinhang Lu, and Warut Suksompong. The price of connectivity in fair division. SIAM Journal on Discrete Mathematics, 36(2):1156-1186, 2022.","title":"The price of connectivity in fair division","authors":"Xiaohui Bei, Ayumi Igarashi, Xinhang Lu, Warut Suksompong","year":"2022","venue":"SIAM Journal on Discrete Mathematics","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Bei et al., 2024] Xiaohui Bei, Alexander Lam, Xinhang Lu, and Warut Suksompong. Welfare loss in connected re- source allocation. CoRR, abs/2405.03467, 2024.","title":"Welfare loss in connected resource allocation","authors":"Xiaohui Bei, Alexander Lam, Xinhang Lu, Warut Suksompong","year":"2024","venue":null,"doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Bertsimas et al., 2011] Dimitris Bertsimas, Vivek F. Farias, and Nikolaos Trichakis. The price of fairness. Operations Research, 59(1):17-31, 2011.","title":"The price of fairness","authors":"Dimitris Bertsimas, F Vivek, Nikolaos Farias, Trichakis","year":"2011","venue":"Operations Research","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Bezáková and Dani, 2005] Ivona Bezáková and Varsha Dani. Allocating indivisible goods. ACM SIGecom Ex- changes, 5(3):11-18, 2005.","title":"Ivona Bezáková and Varsha Dani. Allocating indivisible goods","authors":"Dani Bezáková","year":"2005","venue":"ACM SIGecom Exchanges","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Biggs, 1993] Norman Biggs. Algebraic Graph Theory. Cambridge University Press, 2nd edition, 1993.","title":"Algebraic Graph Theory","authors":"Norman Biggs","year":"1993","venue":null,"doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Bilò et al., 2022] Vittorio Bilò, Ioannis Caragiannis, Michele Flammini, Ayumi Igarashi, Gianpiero Monaco, Dominik Peters, Cosimo Vinci, and William S. Zwicker. Almost envy-free allocations with connected bundles. Games and Economic Behavior, 131:197-221, 2022.","title":"Almost envy-free allocations with connected bundles","authors":"Vittorio Bilò, Ioannis Caragiannis, Michele Flammini, Ayumi Igarashi, Gianpiero Monaco, Dominik Peters, Cosimo Vinci, William S Zwicker","year":"2022","venue":"Games and Economic Behavior","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Biswas and Barman, 2018] Arpita Biswas and Siddharth Barman. Fair division under cardinality constraints. In Proceedings of the 27th International Joint Conference on Artificial Intelligence (IJCAI), pages 91-97, 2018.","title":"Fair division under cardinality constraints","authors":"Arpita Biswas, Siddharth Barman","year":"2018","venue":"Proceedings of the 27th International Joint Conference on Artificial Intelligence (IJCAI)","doi":null,"url":null,"internal_url":"/proceedings/2018/13"},{"position":12,"raw":"[Bollobás, 1998] Béla Bollobás. Modern Graph Theory. Springer, 1998.","title":"Modern Graph Theory","authors":"Béla Bollobás","year":"1998","venue":null,"doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Bondy and Murty, 2008] John A. Bondy and Uppaluri S. R. Murty. Graph Theory. Springer, 2008.","title":"Graph Theory","authors":"John A Bondy, S R Uppaluri, Murty","year":"2008","venue":null,"doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Bouveret et al., 2017] Sylvain Bouveret, Katarína Cechlárová, Edith Elkind, Ayumi Igarashi, and Do- minik Peters. Fair division of a graph. In Proceedings of the 26th International Joint Conference on Artificial Intelligence (IJCAI), pages 135-141, 2017.","title":"Fair division of a graph","authors":"Sylvain Bouveret, Katarína Cechlárová, Edith Elkind, Ayumi Igarashi, Dominik Peters","year":"2017","venue":"Proceedings of the 26th International Joint Conference on Artificial Intelligence (IJCAI)","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Brams and Taylor, 1996] Steven J. Brams and Alan D. Tay- lor. Fair Division: From Cake-Cutting to Dispute Resolu- tion. Cambridge University Press, 1996.","title":"Fair Division: From Cake-Cutting to Dispute Resolution","authors":"Steven J Brams, Alan D Taylor","year":"1996","venue":null,"doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Caragiannis et al., 2012] Ioannis Caragiannis, Christos Kaklamanis, Panagiotis Kanellopoulos, and Maria Ky- ropoulou. The efficiency of fair division. Theory of Computing Systems, 50(4):589-610, 2012.","title":"The efficiency of fair division","authors":"Ioannis Caragiannis, Christos Kaklamanis, Panagiotis Kanellopoulos, Maria","year":"2012","venue":"Theory of Computing Systems","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Caragiannis et al., 2022] Ioannis Caragiannis, Evi Micha, and Nisarg Shah. A little charity guarantees fair con- nected graph partitioning. In Proceedings of the 36th AAAI Conference on Artificial Intelligence (AAAI), pages 4908- 4916, 2022.","title":"A little charity guarantees fair connected graph partitioning","authors":"Ioannis Caragiannis, Evi Micha, Nisarg Shah","year":"2022","venue":"Proceedings of the 36th AAAI Conference on Artificial Intelligence (AAAI)","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Celine et al., 2023] Karen Frilya Celine, Muhammad Ayaz Dzulfikar, and Ivan Adrian Koswara. Egalitarian price of fairness for indivisible goods. In Proceedings of the 20th Pacific Rim International Conference on Artificial Intelli- gence (PRICAI), pages 23-28, 2023.","title":"Egalitarian price of fairness for indivisible goods","authors":"Karen Frilya, Celine, Muhammad Ayaz Dzulfikar, Ivan Adrian Koswara","year":"2023","venue":"Proceedings of the 20th Pacific Rim International Conference on Artificial Intelligence (PRICAI)","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Chartrand and Zhang, 2020] Gary Chartrand and Ping Zhang. Chromatic Graph Theory. CRC Press, Taylor & Francis Group, 2nd edition, 2020.","title":"Chromatic Graph Theory","authors":"Zhang Chartrand, Gary Chartrand, Ping Zhang","year":"2020","venue":null,"doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Dror et al., 2023] Amitay Dror, Michal Feldman, and Erel Segal-Halevi. On fair division under heterogeneous ma- troid constraints. Journal of Artificial Intelligence Re- search, 76:567-611, 2023.","title":"On fair division under heterogeneous matroid constraints","authors":"Amitay Dror, Michal Feldman, Erel Segal-Halevi","year":"2023","venue":"Journal of Artificial Intelligence Research","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Igarashi and Peters, 2019] Ayumi Igarashi and Dominik Pe- ters. Pareto-optimal allocation of indivisible goods with connectivity constraints. In Proceedings of the 33rd AAAI Conference on Artificial Intelligence (AAAI), pages 2045- 2052, 2019.","title":"Ayumi Igarashi and Dominik Peters. Pareto-optimal allocation of indivisible goods with connectivity constraints","authors":"Peters Igarashi","year":"2019","venue":"Proceedings of the 33rd AAAI Conference on Artificial Intelligence (AAAI)","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Igarashi, 2023] Ayumi Igarashi. How to cut a discrete cake fairly. In Proceedings of the 37th AAAI Conference on Artificial Intelligence (AAAI), pages 5681-5688, 2023.","title":"How to cut a discrete cake fairly","authors":"Ayumi Igarashi","year":"2023","venue":"Proceedings of the 37th AAAI Conference on Artificial Intelligence (AAAI)","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Li et al., 2024] Zihao Li, Shengxin Liu, Xinhang Lu, Biaoshuai Tao, and Yichen Tao. A complete landscape for the price of envy-freeness. In Proceedings of the 23rd International Conference on Autonomous Agents and Mul- tiagent Systems (AAMAS), pages 1183-1191, 2024.","title":"A complete landscape for the price of envy-freeness","authors":"Li","year":"2024","venue":"Proceedings of the 23rd International Conference on Autonomous Agents and Multiagent Systems (AAMAS)","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Lonc and Truszczynski, 2020] Zbigniew Lonc and Miroslaw Truszczynski. Maximin share allocations on cycles. Journal of Artificial Intelligence Research, 69:613-655, 2020.","title":"Maximin share allocations on cycles","authors":"Zbigniew Lonc, Miroslaw Truszczynski","year":"2020","venue":"Journal of Artificial Intelligence Research","doi":null,"url":null,"internal_url":"/proceedings/2018/57"},{"position":25,"raw":"[Lonc, 2023] Zbigniew Lonc. Approximating fair division on d-claw-free graphs. In Proceedings of the 32nd Interna- tional Joint Conference on Artificial Intelligence (IJCAI), pages 2826-2834, 2023.","title":"Approximating fair division on d-claw-free graphs","authors":"Zbigniew Lonc","year":"2023","venue":"Proceedings of the 32nd International Joint Conference on Artificial Intelligence (IJCAI)","doi":null,"url":null,"internal_url":"/proceedings/2023/315"},{"position":26,"raw":"[Maon et al., 1986] Yael Maon, Baruch Schieber, and Uzi Vishkin. Parallel ear decomposition search (EDS) and st-numbering in graphs. Theoretical Computer Science, 47:277-298, 1986.","title":"Parallel ear decomposition search (EDS) and st-numbering in graphs","authors":"Maon","year":"1986","venue":"Theoretical Computer Science","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Moulin, 2003] Hervé Moulin. Fair Division and Collective Welfare. MIT Press, 2003.","title":"Fair Division and Collective Welfare","authors":"Hervé Moulin","year":"2003","venue":null,"doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Steinhaus, 1948] Hugo Steinhaus. The problem of fair divi- sion. Econometrica, 16(1):101-104, 1948.","title":"Hugo Steinhaus. The problem of fair division","authors":"Steinhaus","year":"1948","venue":"Econometrica","doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Suksompong, 2019] Warut Suksompong. Fairly allocating contiguous blocks of indivisible items. Discrete Applied Mathematics, 260:227-236, 2019.","title":"Warut Suksompong. Fairly allocating contiguous blocks of indivisible items","authors":"Suksompong","year":"2019","venue":"Discrete Applied Mathematics","doi":null,"url":null,"internal_url":null},{"position":30,"raw":"[Suksompong, 2021] Warut Suksompong. Constraints in fair division. ACM SIGecom Exchanges, 19(2):46-61, 2021.","title":"Warut Suksompong. Constraints in fair division","authors":"Suksompong","year":"2021","venue":"ACM SIGecom Exchanges","doi":null,"url":null,"internal_url":null},{"position":31,"raw":"William Thomson. Introduction to the the- ory of fair allocation. In Felix Brandt, Vincent Conitzer, Ulle Endriss, Jérôme Lang, and Ariel D. Procaccia, ed- itors, Handbook of Computational Social Choice, chap- ter 11, pages 261-283. Cambridge University Press, 2016.","title":"Introduction to the theory of fair allocation","authors":"William Thomson","year":"2016","venue":"Handbook of Computational Social Choice","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}