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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

In contrast to the classical cake-cutting problem (how to fairly divide a desirable object), "chore division" is the problem of how to divide an undesirable object. We develop the first explicit algorithm for envy-free chore division among…

Combinatorics · Mathematics 2009-09-03 Elisha Peterson , Francis Edward Su

We consider the problem of fairly dividing a heterogeneous cake between a number of players with different tastes. In this setting, it is known that fairness requirements may result in a suboptimal division from the social welfare…

Computer Science and Game Theory · Computer Science 2012-05-18 Orit Arzi , Yonatan Aumann , Yair Dombb

In this article we study the problem of fair division. In particular we study a notion introduced by J. Barbanel that generalizes super envy-free fair division. We give a new proof of his result. Our approach allows us to give an explicit…

Computer Science and Game Theory · Computer Science 2017-07-11 Guillaume Chèze , Luca Amodei

We propose an online form of the cake cutting problem. This models situations where agents arrive and depart during the process of dividing a resource. We show that well known fair division procedures like cut-and-choose and the…

Artificial Intelligence · Computer Science 2012-04-18 Toby Walsh

Given a set of n sticks of various (not necessarily different) lengths, what is the largest length so that we can cut k equally long pieces of this length from the given set of sticks? We analyze the structure of this problem and show that…

Data Structures and Algorithms · Computer Science 2017-11-06 Raphael Reitzig , Sebastian Wild

To divide a cake into equal sized pieces most people use a knife and a mixture of luck and dexterity. These attempts are often met with varying success. Through precise geometric constructions performed with the knife replacing Euclid's…

History and Overview · Mathematics 2021-07-13 Alexander Müller-Hermes

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

We study a fair division problem with indivisible items, namely the computation of maximin share allocations. Given a set of $n$ players, the maximin share of a single player is the best she can guarantee to herself, if she would partition…

Computer Science and Game Theory · Computer Science 2016-05-16 Georgios Amanatidis , Georgios Birmpas , Evangelos Markakis

We examine the history of cake cutting mechanisms and discuss the efficiency of their allocations. In the case of piecewise uniform preferences, we define a game that in the presence of strategic agents has equilibria that are not dominated…

Computer Science and Game Theory · Computer Science 2012-04-10 Egor Ianovski

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

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 existence of fair distributions when we have more guests than pieces to allocate, focusing on envy-free distributions among those who receive a piece. The conditions on the demand from the guests can be weakened from those of…

Computer Science and Game Theory · Computer Science 2022-06-16 Pablo Soberón

We propose an online form of the cake cutting problem. This models situations where players arrive and depart during the process of dividing a resource. We show that well known fair division procedures like cut-and-choose and the…

Artificial Intelligence · Computer Science 2010-07-06 Toby Walsh

A collection of objects, some of which are good and some are bad, is to be divided fairly among agents with different tastes, modeled by additive utility functions. If the objects cannot be shared, so that each of them must be entirely…

Computer Science and Game Theory · Computer Science 2022-11-10 Fedor Sandomirskiy , Erel Segal-Halevi

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 this paper, we consider the problem of how to fairly dividing $m$ indivisible chores among $n$ agents. The fairness measure we considered here is the maximin share. The previous best known result is that there always exists a…

Computer Science and Game Theory · Computer Science 2021-06-22 Xin Huang , Pinyan Lu

This work develops algorithmic results for the classic cake-cutting problem in which a divisible, heterogeneous resource (modeled as a cake) needs to be partitioned among agents with distinct preferences. We focus on a standard formulation…

Computer Science and Game Theory · Computer Science 2021-05-13 Siddharth Barman , Nidhi Rathi

We consider fair allocation of indivisible items under an additional constraint: there is an undirected graph describing the relationship between the items, and each agent's share must form a connected subgraph of this graph. This framework…

Computer Science and Game Theory · Computer Science 2017-06-07 Sylvain Bouveret , Katarína Cechlárová , Edith Elkind , Ayumi Igarashi , Dominik Peters

We study the classic cake cutting problem from a mechanism design perspective, in particular focusing on deterministic mechanisms that are strategyproof and fair. We begin by looking at mechanisms that are non-wasteful and primarily show…

Computer Science and Game Theory · Computer Science 2017-05-19 Vijay Menon , Kate Larson