# Equitable Division of a Path

@article{Misra2021EquitableDO, title={Equitable Division of a Path}, author={Neeldhara Misra and Chinmay Sonar and P. R. Vaidyanathan and Rohit Vaish}, journal={ArXiv}, year={2021}, volume={abs/2101.09794} }

We study fair resource allocation under a connectedness constraint wherein a set of indivisible items are arranged on a path and only connected subsets of items may be allocated to the agents. An allocation is deemed fair if it satisfies equitability up to one good (EQ1), which requires that agents’ utilities are approximately equal. We show that achieving EQ1 in conjunction with well-studied measures of economic efficiency (such as Pareto optimality, non-wastefulness, maximum egalitarian or…

## 4 Citations

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We study the problem of dynamically allocating indivisible items to a group of agents in a fair manner. Due to the negative results to achieve fairness when allocations are irrevocable, we allow…

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## References

SHOWING 1-10 OF 50 REFERENCES

### Pareto-Optimal Allocation of Indivisible Goods with Connectivity Constraints

- Economics, Computer ScienceAAAI
- 2019

It is NP-hard to find a Pareto-optimal allocation on a path that satisfies maximin share, but it is shown that a moving-knife algorithm can find such an allocation when agents have binary valuations that have a non-nested interval structure.

### On approximately fair allocations of indivisible goods

- EconomicsEC '04
- 2004

In the presence of indivisibilities, it is shown that there exist allocations in which the envy is bounded by the maximum marginal utility, and an algorithm for computing such allocations is presented.

### Approximating the Nash Social Welfare with Indivisible Items

- EconomicsSIAM J. Comput.
- 2018

We study the problem of allocating a set of indivisible items among agents with additive valuations, with the goal of maximizing the geometric mean of the agents' valuations, i.e., the Nash social…

### Fair Division of a Graph

- Computer ScienceIJCAI
- 2017

It is proved that for acyclic graphs a maximin share allocation always exists and can be found efficiently, and design efficient algorithms for special cases where the underlying graph has simple structure, and/or the number of agents---or, less restrictively, thenumber of agent types---is small.

### Maximin Share Allocations on Cycles

- Economics, MathematicsIJCAI
- 2018

Researchers proved that, unlike in the original problem, in the case of the goods-graph being a tree, allocations offering each agent a bundle of or exceeding her maximin share value always exist and can be found in polynomial time.

### Fair Allocation of Indivisible Goods and Chores

- EconomicsIJCAI
- 2019

This paper considers a more general scenario where an agent may have negative or positive utility for each item, e.g., fair task assignment, where agents can have both positive and negative utilities for each task.

### Chore division on a graph

- MathematicsAutonomous Agents and Multi-Agent Systems
- 2019

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…

### Equitable Allocations of Indivisible Goods

- EconomicsIJCAI
- 2019

This work gives a novel algorithm that guarantees Pareto optimality and equitability up to one good in pseudopolynomial time and shows that approximate envy-freeness, approximate equitability, and Pare to optimality can often be achieved simultaneously.

### Almost Envy-Freeness with General Valuations

- EconomicsSODA
- 2018

This work proves an exponential lower bound on the number of value queries needed to identify an EFX allocation, even for two players with identical valuations, and suggests that there is a rich landscape of problems to explore in the fair division of indivisible goods with different classes of player valuations.