High-Multiplicity Fair Allocation Using Parametric Integer Linear Programming

Bredereck, Robert; Kaczmarczyk, Andrzej; Knop, Dušan; Niedermeier, Rolf

doi:10.48550/arxiv.2005.04907

Cited by 2 publications

(4 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In (Bredereck et al 2020) authors show (theoretical) fixed-parameter tractability results for finding envy-free and…”

Section: Hardnessmentioning

confidence: 99%

See 1 more Smart Citation

Several Stories about High-Multiplicity EFx Allocation (Student Abstract)

Morozov,

Ignatiev,

Dementiev

2024

AAAI

View full text Add to dashboard Cite

Fair division is a topic that has significant social and industrial value. In this work, we study allocations that simultaneously satisfy definitions of fairness and efficiency: EFx and PO. First, we prove that the problem of finding such allocations is NP-hard for two agents. Then, we propose a concept for an ILP-based solving algorithm, the running time of which depends on the number of EFx allocations. We generate input data and analyze algorithm's running time based on the results obtained.

show abstract

“…In (Bredereck et al 2020) authors show (theoretical) fixed-parameter tractability results for finding envy-free and…”

Section: Hardnessmentioning

confidence: 99%

“…This motivated the study of its relaxations. One of the actual and relevant relaxations of EF proposed by (Caragiannis et al 2016) is called envy-free up to any item (EFx). Each agent's bundle should be worth at least as much as any other agent's bundle minus any single item for the allocation to be EFx.…”

Section: Introduction and Related Workmentioning

confidence: 99%

Several Stories about High-Multiplicity EFx Allocation (Student Abstract)

Morozov,

Ignatiev,

Dementiev

2024

AAAI

View full text Add to dashboard Cite

show abstract

“…We are training the network for 10 × 20 and 13 × 26. however, we show our test results for various 𝑛 ×𝑚. We test for network performance for 𝑛 ∈ [7,15]. Further, we also train a individual network over different distributions such as Gaussian (𝜇=0.5,𝜎=1), Log-normal (𝜇 = 0.5,𝜎 = 1), and Exponential (𝜆 = 1), with 150𝑘 training samples for 𝑛 = 10.…”

Section: Training Detailsmentioning

confidence: 99%

“…While finding EF1 or MUW allocations are polynomial-time solvable, maximizing utilitarian welfare within EF1 allocation is an NP-hard problem [2-4, 8, 22] even in additive valuation settings. There is existing work that provides approximate efficiency and fairness guarantees in [1,9,15,35]. But to find allocations that are MUW among EF allocations is an NP-Hard problem even when valuations are additive for two agents [5,8].…”

mentioning

confidence: 99%

EEF1-NN: Efficient and EF1 allocations through Neural Networks

Mishra¹,

Manisha²,

Gujar³

2021

Preprint

View full text Add to dashboard Cite

Neural networks have shown state-of-the-art performance in designing auctions, where the network learns the optimal allocations and payment rule to ensure desirable properties. Motivated by the same, we focus on learning fair division of resources, with no payments involved. Our goal is to allocate the items, goods and/or chores efficiently among the fair allocations. By fair, we mean an allocation that is Envy-free (EF). However, such an allocation may not always exist for indivisible resources. Therefore, we consider the relaxed notion, Envy-freeness up to one item (EF1) that is guaranteed to exist. However, it is not enough to guarantee EF1 since the allocation of empty bundles is also EF1. Hence, we add the further constraint of efficiency, maximum utilitarian social welfare (USW). In general finding, USW allocations among EF1 is an NP-Hard problem even when valuations are additive. In this work, we design a network for this task which we refer to as EEF1-NN. We propose an UNet inspired architecture, Lagrangian loss function, and training procedure to obtain desired results. We show that EEF1-NN finds allocation close to optimal USW allocation and ensures EF1 with a high probability for different distributions over input valuations. Compared to existing approaches EEF1-NN empirically guarantees higher USW. Moreover, EEF1-NN is scalable and determines the allocations much faster than solving it as a constrained optimization problem.

show abstract

High-Multiplicity Fair Allocation Using Parametric Integer Linear Programming

Cited by 2 publications

References 21 publications

Several Stories about High-Multiplicity EFx Allocation (Student Abstract)

Several Stories about High-Multiplicity EFx Allocation (Student Abstract)

EEF1-NN: Efficient and EF1 allocations through Neural Networks

Contact Info

Product

Resources

About