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Sequential allocation is a simple and widely studied mechanism to allocate indivisible items in turns to agents according to a pre-specified picking sequence of agents. At each turn, the current agent in the picking sequence picks its most…

Data Structures and Algorithms · Computer Science 2019-09-17 Mingyu Xiao , Jiaxing Ling

We study the problem of fairly allocating a multiset $M$ of $m$ indivisible items among $n$ agents with additive valuations. Specifically, we introduce a parameter $t$ for the number of distinct types of items and study fair allocations of…

Computer Science and Game Theory · Computer Science 2023-03-30 Pranay Gorantla , Kunal Marwaha , Santhoshini Velusamy

In fair division, equitability dictates that each participant receives the same level of utility. In this work, we study equitable allocations of indivisible goods among agents with additive valuations. While prior work has studied…

Computer Science and Game Theory · Computer Science 2019-05-28 Rupert Freeman , Sujoy Sikdar , Rohit Vaish , Lirong Xia

The problem of fairly allocating a set of indivisible items is a well-known challenge in the field of (computational) social choice. In this scenario, there is a fundamental incompatibility between notions of fairness (such as envy-freeness…

Computer Science and Game Theory · Computer Science 2023-12-21 Ayumi Igarashi , Martin Lackner , Oliviero Nardi , Arianna Novaro

We study the problem of computing maximin share guarantees, a recently introduced fairness notion. Given a set of $n$ agents and a set of goods, the maximin share of a single agent is the best that she can guarantee to herself, if she would…

Computer Science and Game Theory · Computer Science 2018-06-12 Georgios Amanatidis , Evangelos Markakis , Afshin Nikzad , Amin Saberi

We study the problem of allocating a set of indivisible goods to multiple agents. Recent work [Bouveret and Lang, 2011] focused on allocating goods in a sequential way, and studied what is the "best" sequence of agents to pick objects based…

Multiagent Systems · Computer Science 2014-05-27 Wei Huang , Jian Lou , Zhonghua Wen

We study the fair allocation of indivisible goods with variable groups. In this model, the goal is to partition the agents into groups of given sizes and allocate the goods to the groups in a fair manner. We show that for any number of…

Computer Science and Game Theory · Computer Science 2025-11-11 Paul Gölz , Ayumi Igarashi , Pasin Manurangsi , Warut Suksompong

We consider the problem of fair allocation of indivisible goods to agents with submodular valuation functions, where agents may have either equal entitlements or arbitrary (possibly unequal) entitlements. We focus on share-based fairness…

Computer Science and Game Theory · Computer Science 2023-03-23 Gilad Ben Uziahu , Uriel Feige

We analyze the run-time complexity of computing allocations that are both fair and maximize the utilitarian social welfare, defined as the sum of agents' utilities. We focus on two tractable fairness concepts: envy-freeness up to one item…

Computer Science and Game Theory · Computer Science 2024-09-23 Haris Aziz , Xin Huang , Nicholas Mattei , Erel Segal-Halevi

In this work, we revisit the problem of fairly allocating a number of indivisible items that are located on a line to multiple agents. A feasible allocation requires that the allocated items to each agent are connected on the line. The…

Computer Science and Game Theory · Computer Science 2022-05-24 Ankang Sun , Bo Li

We consider the problem of allocating indivisible goods fairly among n agents who have additive and submodular valuations for the goods. Our fairness guarantees are in terms of the maximin share, that is defined to be the maximum value that…

Computer Science and Game Theory · Computer Science 2020-04-07 Siddharth Barman , Sanath Kumar Krishnamurthy

We consider item allocation to individual agents who have additive valuations, in settings in which there are protected groups, and the allocation needs to give each protected group its "fair" share of the total welfare. Informally, within…

Computer Science and Game Theory · Computer Science 2022-04-15 Uriel Feige , Yehonatan Tahan

We consider the problem of fairly and efficiently allocating indivisible items (goods or bads) under capacity constraints. In this setting, we are given a set of categorized items. Each category has a capacity constraint (the same for all…

Computer Science and Game Theory · Computer Science 2023-03-01 Hila Shoshan , Erel Segal-Halevi , Noam Hazon

In this paper, we study the classic problem of fairly allocating indivisible items with the extra feature that the items lie on a line. Our goal is to find a fair allocation that is contiguous, meaning that the bundle of each agent forms a…

Computer Science and Game Theory · Computer Science 2019-04-30 Warut Suksompong

We consider the fair division problem of indivisible items. It is well-known that an envy-free allocation may not exist, and a relaxed version of envy-freeness, envy-freeness up to one item (EF1), has been widely considered. In an EF1…

Computer Science and Game Theory · Computer Science 2022-11-30 Xiaolin Bu , Zihao Li , Shengxin Liu , Jiaxin Song , Biaoshuai Tao

The classic fair division problems assume the resources to be allocated are either divisible or indivisible, or contain a mixture of both, but the agents always have a predetermined and uncontroversial agreement on the (in)divisibility of…

Computer Science and Game Theory · Computer Science 2025-03-31 Xiaohui Bei , Shengxin Liu , Xinhang Lu

In standard fair division models, we assume that all agents are selfish. However, in many scenarios, division of resources has a direct impact on the whole group or even society. Therefore, we study fair allocations of indivisible items…

Computer Science and Game Theory · Computer Science 2025-11-13 Argyris Deligkas , Eduard Eiben , Tiger-Lily Goldsmith , Dušan Knop , Šimon Schierreich

We study the problem of fairly and efficiently allocating a set of items among strategic agents with additive valuations, where items are either all indivisible or all divisible. When items are goods, numerous positive and negative results…

Computer Science and Game Theory · Computer Science 2025-07-08 Bo Li , Biaoshuai Tao , Fangxiao Wang , Xiaowei Wu , Mingwei Yang , Shengwei Zhou

We consider the fair allocation of indivisible items to several agents with additional conflict constraints. These are represented by a conflict graph where each item corresponds to a vertex of the graph and edges in the graph represent…

Discrete Mathematics · Computer Science 2023-08-21 Nina Chiarelli , Matjaž Krnc , Martin Milanič , Ulrich Pferschy , Joachim Schauer

A set of objects is to be divided fairly among agents with different tastes, modeled by additive utility-functions. If we consider the objects as indivisible, many instances of the decision problem: ``Is there a fair division of the objects…

Computer Science and Game Theory · Computer Science 2025-07-03 Samuel Bismuth , Ivan Bliznets , Erel Segal-Halevi