
A Little Charity Guarantees Almost EnvyFreeness
Fair division of indivisible goods is a very wellstudied problem. The g...
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Dividing a Graphical Cake
We consider the classical cakecutting problem where we wish to fairly d...
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Maximin share allocations on cycles
The problem of fair division of indivisible goods is a fundamental probl...
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Multiple Birds with One Stone: Beating 1/2 for EFX and GMMS via Envy Cycle Elimination
Several relaxations of envyfreeness, tailored to fair division in setti...
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Chore division on a graph
The paper considers fair allocation of indivisible nondisposable items t...
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A note on the rationing of divisible and indivisible goods in a general network
The study of matching theory has gained importance recently with applica...
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Comparing Approximate Relaxations of EnvyFreeness
In fair division problems with indivisible goods it is well known that o...
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Connected Fair Allocation of Indivisible Goods
We study the fair allocation of indivisible goods under the assumption that the goods form an undirected graph and each agent must receive a connected subgraph. Our focus is on wellstudied fairness notions including envyfreeness and maximin share fairness. We establish graphspecific maximin share guarantees, which are tight for large classes of graphs in the case of two agents and for paths and stars in the general case. Unlike in previous work, our guarantees are with respect to the completegraph maximin share, which allows us to compare possible guarantees for different graphs. For instance, we show that for biconnected graphs it is possible to obtain at least 3/4 of the maximin share, while for the remaining graphs the guarantee is at most 1/2. In addition, we determine the optimal relaxation of envyfreeness that can be obtained with each graph for two agents, and characterize the set of trees and complete bipartite graphs that always admit an allocation satisfying envyfreeness up to one good (EF1) for three agents. Our work demonstrates several applications of graphtheoretical tools and concepts to fair division problems.
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