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Related papers: On Connected Strongly-Proportional Cake-Cutting

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We study the disproportionate version of the classical cake-cutting problem: how efficiently can we divide a cake, here $[0,1]$, among $n$ agents with different demands $\alpha_1, \alpha_2, \dots, \alpha_n$ summing to $1$? When all the…

Combinatorics · Mathematics 2019-09-17 Logan Crew , Bhargav Narayanan , Sophie Spirkl

In the classic cake-cutting problem (Steinhaus, 1948), a heterogeneous resource has to be divided among n agents with different valuations in a proportional way --- giving each agent a piece with a value of at least 1/n of the total. In…

Computer Science and Game Theory · Computer Science 2017-06-05 Erel Segal-Halevi , Balázs Sziklai

We study the classic problem of \emph{fairly} dividing a heterogeneous and divisible resource -- modeled as a line segment $[0,1]$ and typically called as a \emph{cake} -- among $n$ agents. This work considers an interesting variant of the…

Computer Science and Game Theory · Computer Science 2022-11-15 Ganesh Ghalme , Xin Huang , Yuka Machino , Nidhi Rathi

The classic cake-cutting problem provides a model for addressing the fair and efficient allocation of a divisible, heterogeneous resource among agents with distinct preferences. Focusing on a standard formulation of cake cutting, in which…

Machine Learning · Computer Science 2021-11-30 Mohammad Ghodsi , Amirmahdi Mirfakhar

In the classical cake cutting problem, a resource must be divided among agents with different utilities so that each agent believes they have received a fair share of the resource relative to the other agents. We introduce a variant of the…

Data Structures and Algorithms · Computer Science 2018-02-27 Rediet Abebe , Jon Kleinberg , David Parkes

In the envy-free cake-cutting problem we are given a resource, usually called a cake and represented as the $[0,1]$ interval, and a set of $n$ agents with heterogeneous preferences over pieces of the cake. The goal is to divide the cake…

Computer Science and Game Theory · Computer Science 2025-09-01 Alexandros Hollender , Aviad Rubinstein

Austin's moving knife procedure was originally introduced to find a consensus division of an interval/circular cake between two agents, each of whom believes that they receive exactly half of the cake. We generalise this in two ways: we…

Combinatorics · Mathematics 2025-09-26 Josef Hanke , Ana Rita Pires

Cake cutting is a classic fair division problem, with the cake serving as a metaphor for a heterogeneous divisible resource. Recently, it was shown that for any number of players with arbitrary preferences over a cake, it is possible to…

Theoretical Economics · Economics 2023-03-20 Erel Segal-Halevi , Warut Suksompong

In this paper, we consider the classic fair division problem of allocating $m$ divisible items to $n$ agents with linear valuations over the items. We define novel notions of fair shares from the perspective of individual agents via the…

Computer Science and Game Theory · Computer Science 2024-11-18 Yannan Bai , Kamesh Munagala , Yiheng Shen , Ian Zhang

Single minded agents have strict preferences, in which a bundle is acceptable only if it meets a certain demand. Such preferences arise naturally in scenarios such as allocating computational resources among users, where the goal is to…

Computer Science and Game Theory · Computer Science 2016-04-29 Simina Brânzei , Yuezhou Lv , Ruta Mehta

The classic cake cutting problem concerns the fair allocation of a heterogeneous resource among interested agents. In this paper, we study a public goods variant of the problem, where instead of competing with one another for the cake, the…

Computer Science and Game Theory · Computer Science 2025-01-31 Xiaohui Bei , Xinhang Lu , Warut Suksompong

Cake-cutting is a playful name for the fair division of a heterogeneous, divisible good among agents, a well-studied problem at the intersection of mathematics, economics, and artificial intelligence. The cake-cutting literature is rich and…

Computer Science and Game Theory · Computer Science 2023-11-23 Peter Kern , Daniel Neugebauer , Jörg Rothe , René L. Schilling , Dietrich Stoyan , Robin Weishaupt

We study the problem of fair division of a set of indivisible goods with connectivity constraints. Specifically, we assume that the goods are represented as vertices of a connected graph, and sets of goods allocated to the agents are…

Discrete Mathematics · Computer Science 2025-08-18 Václav Blažej , Michał Dębski , Zbigniew Lonc , Marta Piecyk , Paweł Rzążewski

A perfectly divisible cake is to be divided among a group of agents. Each agent is entitled to a share between zero and one, and these entitlements are compatible in that they sum to one. The mediator does not know the preferences of the…

Theoretical Economics · Economics 2025-08-13 Florian Brandl , Andrew Mackenzie

Classic cake-cutting algorithms enable people with different preferences to divide among them a heterogeneous resource (``cake''), such that the resulting division is fair according to each agent's individual preferences. However, these…

Computer Science and Game Theory · Computer Science 2021-08-06 Erel Segal-Halevi , Shmuel Nitzan , Avinatan Hassidim , Yonatan Aumann

We consider the problem of envy-free cake cutting, which is the distribution of a continuous heterogeneous resource among self interested players such that nobody prefers what somebody else receives to what they get. Existing work has…

Computer Science and Game Theory · Computer Science 2018-01-26 Eshwar Ram Arunachaleswaran , Ragavendran Gopalakrishnan

Cutting a cake is a metaphor for the problem of dividing a resource (cake) among several agents. The problem becomes non-trivial when the agents have different valuations for different parts of the cake (i.e. one agent may like chocolate…

Information Theory · Computer Science 2016-01-26 Payam Delgosha , Amin Gohari

We study the paradigmatic fair division problem of allocating a divisible good among agents with heterogeneous preferences, commonly known as cake cutting. Classical cake cutting protocols are susceptible to manipulation. Do their strategic…

Computer Science and Game Theory · Computer Science 2016-07-20 Simina Brânzei , Ioannis Caragiannis , David Kurokawa , Ariel D. Procaccia

We study searching and sorting in rounds motivated by a fair division question: given a cake cutting problem with $n$ players, compute a fair allocation in at most $k$ rounds of interaction with the players. Rounds interpolate between the…

Data Structures and Algorithms · Computer Science 2023-11-21 Simina Brânzei , Dimitris Paparas , Nicholas Recker

We study the problem of allocating indivisible items to agents with additive valuations, under the additional constraint that bundles must be connected in an underlying item graph. Previous work has considered the existence and complexity…

Computer Science and Game Theory · Computer Science 2018-11-13 Ayumi Igarashi , Dominik Peters