English
Related papers

Related papers: Connected Equitable Cake Division via Sperner's Le…

200 papers

We study fair allocation of indivisible chores (i.e., items with non-positive value) among agents with additive valuations. An allocation is deemed fair if it is (approximately) equitable, which means that the disutilities of the agents are…

Computer Science and Game Theory · Computer Science 2020-02-27 Rupert Freeman , Sujoy Sikdar , Rohit Vaish , Lirong Xia

We consider the classic cake cutting problem in the Robertson-Webb model, with the objective of proportional fairness. We show that any randomized algorithm must use $\Omega(n \log n)$ queries.

Data Structures and Algorithms · Computer Science 2026-05-22 Stephen Arndt , Kirk Pruhs , Trung Tran

We consider the problem of fairly dividing a set of heterogeneous divisible resources among agents with different preferences. We focus on the setting where the resources correspond to the edges of a connected graph, every agent must be…

Data Structures and Algorithms · Computer Science 2023-12-13 Argyrios Deligkas , Eduard Eiben , Robert Ganian , Thekla Hamm , Sebastian Ordyniak

We study the problem of dividing a multi-layered cake under non-overlapping constraints. This problem, recently proposed by Hosseini et al. (IJCAI, 2020), captures several natural scenarios such as the allocation of multiple facilities over…

Computer Science and Game Theory · Computer Science 2022-12-22 Ayumi Igarashi , Frédéric Meunier

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

Inheritances, divorces or liquidations of companies require common assets to be divided among the entitled parties. Legal methods usually consider the market value of goods, while fair division theory takes into account the parties'…

Computer Science and Game Theory · Computer Science 2023-05-10 Marco Dall'Aglio

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 following cake cutting game: Alice chooses a set P of n points in the square (cake) [0,1]^2, where (0,0) is in P; Bob cuts out n axis-parallel rectangles with disjoint interiors, each of them having a point of P as the lower…

Computational Geometry · Computer Science 2011-04-04 Tobias Christ , Andrea Francke , Heidi Gebauer , Jiří Matoušek , Takeaki Uno

Relying on configuration spaces and equivariant topology, we study a general "cooperative envy-free division problem". A group of players want to cut a "cake" $I=[0,1]$ and divide among themselves the pieces in an envy-free manner. Once the…

Combinatorics · Mathematics 2023-02-08 Duško Jojić , Gaiane Panina , Rade Živaljević

The paper considers fair allocation of indivisible nondisposable items that generate disutility (chores). We assume that these items are placed in the vertices of a graph and each agent's share has to form a connected subgraph of this…

Artificial Intelligence · Computer Science 2018-12-06 Sylvain Bouveret , Katarína Cechlárová , Julien Lesca

We study an online model of fair division designed to capture features of a real world charity problem. We consider two simple mechanisms for this model in which agents simply declare what items they like. We analyse several axiomatic…

Computer Science and Game Theory · Computer Science 2015-03-03 Martin Aleksandrov , Haris Aziz , Serge Gaspers , Toby Walsh

We prove existence of envy-free allocations in markets with heterogenous indivisible goods and money, when a given quantity is supplied from each of the goods and agents have unit demands. We depart from most of the previous literature by…

Computer Science and Game Theory · Computer Science 2014-06-26 Yaron Azrieli , Eran Shmaya

Fair division considers the allocation of scarce resources among agents in such a way that every agent gets a fair share. It is a fundamental problem in society and has received significant attention and rapid developments from the game…

Computer Science and Game Theory · Computer Science 2024-08-13 Shengxin Liu , Xinhang Lu , Mashbat Suzuki , Toby Walsh

We study the cake-cutting problem when agents have single-peaked preferences over the cake. We show that a recently proposed mechanism by Wang-Wu (2019) to obtain envy-free allocations can yield large welfare losses. Using a simplifying…

Computer Science and Game Theory · Computer Science 2020-03-05 Bhavook Bhardwaj , Rajnish Kumar , Josue Ortega

We study the problem of finding an envy-free allocation of indivisible goods among agents with additive valuations. We focus on the fairness notion of envy-freeness up to any good (EFX). A central open question in fair division is whether…

Computer Science and Game Theory · Computer Science 2025-05-26 Vishwa Prakash HV , Pratik Ghosal , Prajakta Nimbhorkar , Nithin Varma

In cake-cutting, strategy-proofness is a very costly requirement in terms of fairness: for n=2 it implies a dictatorial allocation, whereas for n > 2 it requires that one agent receives no cake. We show that a weaker version of this…

Computer Science and Game Theory · Computer Science 2019-10-15 Josue Ortega , Erel Segal-Halevi

We study the problem of Envy-Free Incomplete Connected Fair Division, where exactly p vertices of an undirected graph must be allocated to agents such that each agent receives a connected share and does not envy another agent's share.…

Data Structures and Algorithms · Computer Science 2025-12-30 Ajaykrishnan E S , Daniel Lokshtanov

A pizza is a pair of planar convex bodies $A\subseteq B$,where $B$ represents the dough and $A$ the topping of the pizza. A partition of a pizza by straight lines is a succession of double operations:a cut by a full straight line, followed…

Metric Geometry · Mathematics 2015-09-15 Augustin Fruchard , Alexander Magazinov

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

We study the computational complexity of finding fair allocations of indivisible goods in the setting where a social network on the agents is given. Notions of fairness in this context are "localized", that is, agents are only concerned…

Computer Science and Game Theory · Computer Science 2021-11-24 Neeldhara Misra , Debanuj Nayak