Warut Suksompong
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Abstract
The fair allocation of resources to interested agents is a fundamental problem in society. While the majority of the fair division literature assumes that all allocations are feasible, in practice there are often constraints on the allocation that can be chosen. In this survey, we discuss fairness guarantees for both divisible (cake cutting) and indivisible resources under several common types of constraints, including connectivity, cardinality, matroid, geometric, separation, budget, and conflict constraints. We also outline a number of open questions and directions.
- Arunachaleswaran, E. R., Barman, S., Kumar, R., and Rathi, N. 2019. Fair and efficient cake division with connected pieces. In Proceedings of the 15th Conference on Web and Internet Economics (WINE). 57--70. Extended version available at CoRR abs/1907.11019.Google Scholar
- Arunachaleswaran, E. R. and Gopalakrishnan, R. 2018. The price of indivisibility in cake cutting. CoRR abs/1801.08341.Google Scholar
- Aziz, H., Caragiannis, I., Igarashi, A., and Walsh, T. 2019. Fair allocation of indivisible goods and chores. In Proceedings of the 28th International Joint Conference on Artificial Intelligence (IJCAI). 53--59. Google ScholarDigital Library
- Aziz, H. and Mackenzie, S. 2016. A discrete and bounded envy-free cake cutting protocol for any number of agents. In Proceedings of the 57th Annual Symposium on Foundations of Computer Science (FOCS). 416--427. Google ScholarDigital Library
- Babaioff, M., Nisan, N., and Talgam-Cohen, I. 2021. Competitive equilibrium with indivisible goods and generic budgets. Mathematics of Operations Research 46, 1, 382--403.Google ScholarDigital Library
- Bei, X., Igarashi, A., Lu, X., and Suksompong, W. 2021. The price of connectivity in fair division. In Proceedings of the 35th AAAI Conference on Artificial Intelligence (AAAI). 5151--5158.Google Scholar
- Bei, X., Li, Z., Liu, J., Liu, S., and Lu, X. 2021. Fair division of mixed divisible and indivisible goods. Artificial Intelligence 293, 103436.Google ScholarCross Ref
- Bei, X. and Suksompong, W. 2021. Dividing a graphical cake. In Proceedings of the 35th AAAI Conference on Artificial Intelligence (AAAI). 5159--5166.Google Scholar
- Bilò, V., Caragiannis, I., Flammini, M., Igarashi, A., Monaco, G., Peters, D., Vinci, C., and Zwicker, W. S. 2019. Almost envy-free allocations with connected bundles. In Proceedings of the 10th Innovations in Theoretical Computer Science Conference (ITCS). 14:1--14:21.Google Scholar
- Biswas, A. and Barman, S. 2018. Fair division under cardinality constraints. In Proceedings of the 27th International Joint Conference on Artificial Intelligence (IJCAI). 91--97. Extended version available at CoRR abs/1804.09521. Google ScholarDigital Library
- Bogomolnaia, A., Moulin, H., Sandomirskiy, F., and Yanovskaya, E. 2017. Competitive division of a mixed manna. Econometrica 85, 6, 1847--1871.Google ScholarCross Ref
- Bouveret, S., Cechlárová, K., Elkind, E., Igarashi, A., and Peters, D. 2017. Fair division of a graph. In Proceedings of the 26th International Joint Conference on Artificial Intelligence (IJCAI). 135--141. Google ScholarDigital Library
- Bouveret, S., Cechlárová, K., and Lesca, J. 2019. Chore division on a graph. Autonomous Agents and Multi-Agent Systems 33, 5, 540--563.Google ScholarDigital Library
- Bouveret, S., Chevaleyre, Y., and Maudet, N. 2016. Fair allocation of indivisible goods. In Handbook of Computational Social Choice, F. Brandt, V. Conitzer, U. Endriss, J. Lang, and A. D. Procaccia, Eds. Cambridge University Press, Chapter 12, 284--310.Google Scholar
- Brams, S. J. and Taylor, A. D. 1996. Fair Division: From Cake-Cutting to Dispute Resolution. Cambridge University Press.Google ScholarCross Ref
- Brânzei, S. and Nisan, N. 2017. The query complexity of cake cutting. CoRR abs/1705.02946.Google Scholar
- Caragiannis, I., Kurokawa, D., Moulin, H., Procaccia, A. D., Shah, N., and Wang, J. 2019. The unreasonable fairness of maximum Nash welfare. ACM Transactions on Economics and Computation 7, 3, 12:1--12:32. Google ScholarDigital Library
- Chakraborty, M., Igarashi, A., Suksompong, W., and Zick, Y. 2021. Weighted envy-freeness in indivisible item allocation. ACM Transactions on Economics and Computation 9, 3, 18:1--18:39. Google ScholarDigital Library
- Chiarelli, N., Krnc, M., Milanič, M., Pferschy, U., Pivač, N., and Schauer, J. 2020. Fair packing of independent sets. In Proceedings of the 31st International Workshop on Combinatorial Algorithms (IWOCA). 154--165.Google Scholar
- Cseh, A. and Fleiner, T. 2020. The complexity of cake cutting with unequal shares. ACM Transactions on Algorithms 16, 3, 29:1--29:21. Google ScholarDigital Library
- Deng, X., Qi, Q., and Saberi, A. 2012. Algorithmic solutions for envy-free cake cutting. Operations Research 60, 6, 1461--1476.Google ScholarDigital Library
- Dror, A., Feldman, M., and Segal-Halevi, E. 2021. On fair division under heterogeneous matroid constraints. In Proceedings of the 35th AAAI Conference on Artificial Intelligence (AAAI). 5312--5320.Google Scholar
- Dubins, L. E. and Spanier, E. H. 1961. How to cut a cake fairly. American Mathematical Monthly 68, 1, 1--17.Google ScholarCross Ref
- Edmonds, J. and Pruhs, K. 2011. Cake cutting really is not a piece of cake. ACM Transactions on Algorithms 7, 4, 51:1--51:12. Google ScholarDigital Library
- Elkind, E., Segal-Halevi, E., and Suksompong, W. 2021a. Graphical cake cutting via maximin share. In Proceedings of the 30th International Joint Conference on Artificial Intelligence (IJCAI). 161--167.Google Scholar
- Elkind, E., Segal-Halevi, E., and Suksompong, W. 2021b. Keep your distance: Land division with separation. In Proceedings of the 30th International Joint Conference on Artificial Intelligence (IJCAI). 168--174.Google Scholar
- Elkind, E., Segal-Halevi, E., and Suksompong, W. 2021c. Mind the gap: Cake cutting with separation. In Proceedings of the 35th AAAI Conference on Artificial Intelligence (AAAI). 5330--5338.Google Scholar
- Even, S. and Paz, A. 1984. A note on cake cutting. Discrete Applied Mathematics 7, 3, 285--296.Google ScholarCross Ref
- Farhadi, A., Ghodsi, M., Hajiaghayi, M., Lahaie, S., Pennock, D., Seddighin, M., Seddighin, S., and Yami, H. 2019. Fair allocation of indivisible goods to asymmetric agents. Journal of Artificial Intelligence Research 64, 1--20. Google ScholarDigital Library
- Gan, J., Li, B., and Wu, X. 2021. Approximately envy-free budget-feasible allocation. CoRR abs/2106.14446.Google Scholar
- Garg, N., Kavitha, T., Kumar, A., Mehlhorn, K., and Mestre, J. 2010. Assigning papers to referees. Algorithmica 58, 1, 119--136.Google ScholarDigital Library
- Goldberg, P. W., Hollender, A., and Suksompong, W. 2020. Contiguous cake cutting: Hardness results and approximation algorithms. Journal of Artificial Intelligence Research 69, 109--141.Google ScholarCross Ref
- Goldman, J. and Procaccia, A. D. 2014. Spliddit: Unleashing fair division algorithms. ACM SIGecom Exchanges 13, 2, 41--46. Google ScholarDigital Library
- Gourvès, L. and Monnot, J. 2019. On maximin share allocations in matroids. Theoretical Computer Science 754, 50--64.Google ScholarCross Ref
- Gourvès, L., Monnot, J., and Tlilane, L. 2014. Near fairness in matroids. In Proceedings of the 21st European Conference on Artificial Intelligence (ECAI). 393--398. Google ScholarDigital Library
- Hosseini, H., Igarashi, A., and Searns, A. 2020. Fair division of time: Multi-layered cake cutting. In Proceedings of the 29th International Joint Conference on Artificial Intelligence (IJCAI). 182--188. Google ScholarDigital Library
- Hummel, H. and Hetland, M. L. 2021a. Fair allocation of conflicting items. CoRR abs/2104.06280.Google Scholar
- Hummel, H. and Hetland, M. L. 2021b. Guaranteeing half-maximin shares under cardinality constraints. CoRR abs/2106.07300.Google Scholar
- Igarashi, A. and Meunier, F. 2021. Envy-free division of multi-layered cakes. In Proceedings of the 17th Conference on Web and Internet Economics (WINE). Forthcoming.Google Scholar
- Igarashi, A. and Peters, D. 2019. Pareto-optimal allocation of indivisible goods with connectivity constraints. In Proceedings of the 33rd AAAI Conference on Artificial Intelligence (AAAI). 2045--2052.Google Scholar
- Igarashi, A. and Zwicker, W. S. 2021. Fair division of graphs and of tangled cakes. CoRR abs/2102.08560.Google Scholar
- Jojić, D., Panina, G., and Živaljević, R. 2021. Splitting necklaces, with constraints. SIAM Journal on Discrete Mathematics 35, 2, 1268--1286.Google ScholarCross Ref
- Kyropoulou, M., Suksompong, W., and Voudouris, A. A. 2020. Almost envy-freeness in group resource allocation. Theoretical Computer Science 841, 110--123.Google ScholarCross Ref
- Li, Z. and Vetta, A. 2021. The fair division of hereditary set systems. ACM Transactions on Economics and Computation 9, 2, 12:1--12:19. Google ScholarDigital Library
- Lipton, R. J., Markakis, E., Mossel, E., and Saberi, A. 2004. On approximately fair allocations of indivisible goods. In Proceedings of the 5th ACM Conference on Electronic Commerce (EC). 125--131. Google ScholarDigital Library
- Lonc, Z. and Truszczynski, M. 2020. Maximin share allocations on cycles. Journal of Artificial Intelligence Research 69, 613--655.Google ScholarCross Ref
- Manurangsi, P. and Suksompong, W. 2017. Asymptotic existence of fair divisions for groups. Mathematical Social Sciences 89, 100--108.Google ScholarCross Ref
- Markakis, E. 2017. Approximation algorithms and hardness results for fair division. In Trends in Computational Social Choice, U. Endriss, Ed. AI Access, Chapter 12, 231--247.Google Scholar
- Misra, N., Sonar, C., Vaidyanathan, P. R., and Vaish, R. 2021. Equitable division of a path. CoRR abs/2101.09794.Google Scholar
- Moulin, H. 2003. Fair Division and Collective Welfare. MIT Press.Google Scholar
- Procaccia, A. D. 2016. Cake cutting algorithms. In Handbook of Computational Social Choice, F. Brandt, V. Conitzer, U. Endriss, J. Lang, and A. D. Procaccia, Eds. Cambridge University Press, Chapter 13, 311--329.Google Scholar
- Robertson, J. and Webb, W. 1998. Cake-Cutting Algorithms: Be Fair if You Can. Peters/CRC Press.Google Scholar
- Segal-Halevi, E. 2018. Fairly dividing a cake after some parts were burnt in the oven. In Proceedings of the 17th International Conference on Autonomous Agents and Multiagent Systems (AAMAS). 1276--1284. Google ScholarDigital Library
- Segal-Halevi, E. 2021. Fair multi-cake cutting. Discrete Applied Mathematics 291, 15--35.Google ScholarCross Ref
- Segal-Halevi, E., Hassidim, A., and Aumann, Y. 2020. Envy-free division of land. Mathematics of Operations Research 45, 3, 896--922.Google ScholarCross Ref
- Segal-Halevi, E. and Nitzan, S. 2019. Envy-free cake-cutting among families. Social Choice and Welfare 53, 4, 709--740.Google ScholarCross Ref
- Segal-Halevi, E., Nitzan, S., Hassidim, A., and Aumann, Y. 2017. Fair and square: Cake-cutting in two dimensions. Journal of Mathematical Economics 70, 8, 1--28.Google ScholarCross Ref
- Shah, N. 2017. Spliddit: Two years of making the world fairer. XRDS: Crossroads, The ACM Magazine for Students 24, 1, 24--28. Google ScholarDigital Library
- Stromquist, W. 1980. How to cut a cake fairly. American Mathematical Monthly 87, 8, 640--644.Google ScholarCross Ref
- Stromquist, W. 2008. Envy-free cake divisions cannot be found by finite protocols. Electronic Journal of Combinatorics 15, #R11.Google ScholarCross Ref
- Su, F. E. 1999. Rental harmony: Sperner's lemma in fair division. American Mathematical Monthly 106, 10, 930--942.Google ScholarCross Ref
- Suksompong, W. 2018. Approximate maximin shares for groups of agents. Mathematical Social Sciences 92, 40--47.Google ScholarCross Ref
- Suksompong, W. 2019. Fairly allocating contiguous blocks of indivisible items. Discrete Applied Mathematics 260, 227--236.Google ScholarDigital Library
- Thomson, W. 2016. Introduction to the theory of fair allocation. In Handbook of Computational Social Choice, F. Brandt, V. Conitzer, U. Endriss, J. Lang, and A. D. Procaccia, Eds. Cambridge University Press, Chapter 11, 261--283.Google Scholar
- Walsh, T. 2020. Fair division: the computer scientist's perspective. In Proceedings of the 29th International Joint Conference on Artificial Intelligence (IJCAI). 4966--4972. Google ScholarDigital Library
- Wu, X., Li, B., and Gan, J. 2021. Budget-feasible maximum Nash social welfare allocation is almost envy-free. In Proceedings of the 30th International Joint Conference on Artificial Intelligence (IJCAI). 465--471.Google Scholar
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- Constraints in fair division
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