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Related papers: Envy-free division using mapping degree

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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

Motivated by the controller placement problems in software-defined networks and the fair division principles of classical "cake cutting", we investigate the following two-player zero-sum game. In our model, a defender places a limited…

Computational Complexity · Computer Science 2026-05-19 Grzegorz Gutowski , Konstanty Junosza-Szaniawski , Antonio Lauerbach , Alexander Wolff

We consider the classic problem of envy-free division of a heterogeneous good ("cake") among several agents. It is known that, when the allotted pieces must be connected, the problem cannot be solved by a finite algorithm for 3 or more…

Data Structures and Algorithms · Computer Science 2018-05-15 Erel Segal-Halevi , Avinatan Hassidim , Yonatan Aumann

We study the envy-free cake-cutting problem for $d+1$ players with $d$ cuts, for both the oracle function model and the polynomial time function model. For the former, we derive a $\theta(({1\over\epsilon})^{d-1})$ time matching bound for…

Computer Science and Game Theory · Computer Science 2009-07-10 Xiaotie Deng , Qi Qi , Amin Saberi

Cake-cutting protocols aim at dividing a ``cake'' (i.e., a divisible resource) and assigning the resulting portions to several players in a way that each of the players feels to have received a ``fair'' amount of the cake. An important…

Computer Science and Game Theory · Computer Science 2009-10-19 Claudia Lindner , Joerg Rothe

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

Computer Science and Game Theory · Computer Science 2021-05-21 Eshwar Ram Arunachaleswaran , Siddharth Barman , Rachitesh Kumar , Nidhi Rathi

We initiate the study of multi-layered cake cutting with the goal of fairly allocating multiple divisible resources (layers of a cake) among a set of agents. The key requirement is that each agent can only utilize a single resource at each…

Computer Science and Game Theory · Computer Science 2020-04-29 Hadi Hosseini , Ayumi Igarashi , Andrew Searns

We introduce a graphical framework for fair division in cake cutting, where comparisons between agents are limited by an underlying network structure. We generalize the classical fairness notions of envy-freeness and proportionality to this…

Data Structures and Algorithms · Computer Science 2017-07-10 Xiaohui Bei , Youming Qiao , Shengyu Zhang

Envy-freeness is one of the most prominent fairness concepts in the allocation of indivisible goods. Even though trivial envy-free allocations always exist, rich literature shows this is not true when one additionally requires some…

Computer Science and Game Theory · Computer Science 2025-02-19 Robert Bredereck , Andrzej Kaczmarczyk , Junjie Luo , Bin Sun

We consider a fair division setting in which $m$ indivisible items are to be allocated among $n$ agents, where the agents have additive utilities and the agents' utilities for individual items are independently sampled from a distribution.…

Computer Science and Game Theory · Computer Science 2023-03-20 Pasin Manurangsi , Warut Suksompong

We study a fair division setting in which participants are to be fairly distributed among teams, where not only do the teams have preferences over the participants as in the canonical fair division setting, but the participants also have…

Computer Science and Game Theory · Computer Science 2024-08-27 Ayumi Igarashi , Yasushi Kawase , Warut Suksompong , Hanna Sumita

Given a set of $p$ players we consider problems concerning envy-free allocation of collections of $k$ pieces from a given set of goods or chores. We show that if $p\le n$ and each player can choose $k$ pieces out of $n$ pieces of a cake,…

Combinatorics · Mathematics 2017-10-27 Kathryn Nyman , Francis Edward Su , Shira Zerbib

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

The problem of fair division known as "cake cutting" has been the focus of multiple papers spanning several decades. The most prominent problem in this line of work has been to bound the query complexity of computing an envy-free outcome in…

Computer Science and Game Theory · Computer Science 2022-01-14 Ioannis Caragiannis , Vasilis Gkatzelis , Alexandros Psomas , Daniel Schoepflin

The fair allocation of scarce resources is a central problem in mathematics, computer science, operations research, and economics. While much of the fair-division literature assumes that individuals have underlying cardinal preferences,…

Computer Science and Game Theory · Computer Science 2026-03-02 Trung Dang , Daniel Halpern , Anuran Makur , Alexandros Psomas , Japneet Singh , Paritosh Verma

The Seat Arrangement Problem is a problem of finding a desirable seat arrangement for given preferences of agents and a seat graph that represents a configuration of seats. In this paper, we consider decision problems of determining if an…

Computer Science and Game Theory · Computer Science 2025-01-14 Sota Kawase , Shuichi Miyazaki

We consider the problem of allocating a distribution of items to $n$ recipients where each recipient has to be allocated a fixed, prespecified fraction of all items, while ensuring that each recipient does not experience too much envy. We…

Computer Science and Game Theory · Computer Science 2022-10-03 Steven Yin , Christian Kroer

We study the problem of fair division when the resources contain both divisible and indivisible goods. Classic fairness notions such as envy-freeness (EF) and envy-freeness up to one good (EF1) cannot be directly applied to the mixed goods…

Computer Science and Game Theory · Computer Science 2021-01-28 Xiaohui Bei , Zihao Li , Jinyan Liu , Shengxin Liu , Xinhang Lu

Two-sided matching, such as matching between students and schools, has been applied to various aspects of real life and has been the subject of much research, however, it has been plagued by the fact that efficiency and fairness are…

Computer Science and Game Theory · Computer Science 2025-08-22 Ryota Takeshima , Kei Kimura , Ayumu Kuroki , Temma Wakasugi , Makoto Yokoo

Fair division has emerged as a very hot topic in multiagent systems, and envy-freeness is among the most compelling fairness concepts. An allocation of indivisible items to agents is envy-free if no agent prefers the bundle of any other…

Computer Science and Game Theory · Computer Science 2021-02-26 Ioannis Caragiannis , Stavros Ioannidis