Fair allocation of indivisible goods: Beyond additive valuations

Ghodsi, Mohammad; Hajiaghayi, MohammadTaghi; Seddighin, Masoud; Seddighin, Saeed; Yami, Hadi

doi:10.1016/j.artint.2021.103633

Cited by 13 publications

(11 citation statements)

References 16 publications

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“…Surprisingly, we show that n-approximation is the best possible even when the valuations are submodular. This result exhibits a significant difference between the allocations of chores and goods, since for goods with submodular (even XoS) valuations, we always have constant-approximate MMS fair allocations (Barman and Krishnamurthy, 2020;Ghodsi et al, 2022).…”

Section: Resultsmentioning

confidence: 94%

“…Beyond additive valuations, Barman and Krishnamurthy (2020) initiated the study of approximate MMS fair allocation with submodular valuations, and proved that a 0.21-approximate MMS fair allocation can be computed by the round-robin algorithm. Ghodsi et al (2022) improved the approximation ratio to 1/3, and moreover, they gave constant and logarithmic approximation guarantees for XOS and subadditive valuations, respectively. The approximations for XOS and subadditive valuations are recently improved in .…”

Section: Introduction 1background and Related Researchmentioning

confidence: 96%

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Fair Allocation of Indivisible Chores: Beyond Additive Valuations

Li¹,

Wang²,

Zhou³

2022

Preprint

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In this work, we study the maximin share (MMS) fair allocation of indivisible chores. For additive valuations, Huang and Lu [EC, 2021] designed an algorithm to compute a 11/9-approximate MMS fair allocation, and Feige et al. [WINE, 2021] proved that no algorithm can achieve better than 44/43 approximation. Beyond additive valuations, unlike the allocation of goods, very little is known. We first prove that for submodular valuations, in contrast to the allocation of goods where constant approximations are proved by Barman and Krishnamurthy [TEAC, 2020] and Ghodsi et al [AIJ, 2022], the best possible approximation ratio is n. We then focus on two concrete settings where the valuations are combinatorial. In the first setting, agents need to use bins to pack a set of items where the items may have different sizes to different agents and the agents want to use as few bins as possible to pack the items assigned to her. In the second setting, each agent has a set of machines that can be used to process a set of items, and the objective is to minimize the makespan of processing the items assigned to her. For both settings, we design constant approximation algorithms, and show that if the fairness notion is changed to proportionality up to one/any item, the best approximation ratio is n.

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Section: Resultsmentioning

confidence: 94%

Section: Introduction 1background and Related Researchmentioning

confidence: 96%

Fair Allocation of Indivisible Chores: Beyond Additive Valuations

Li¹,

Wang²,

Zhou³

2022

Preprint

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“…On the negative side, recently showed that it is impossible to achieve an approximation bound better than 39/40. Barman and Krishnamurthy [2020] and Ghodsi et al [2022] designed algorithms for computing approximate MMS allocations for richer classes of valuations (such as submodular, XOS, and subadditive). Open Problem 5.…”

Section: Relaxations Of Efxmentioning

confidence: 99%

Fair Division of Indivisible Goods: A Survey

Cerutti

Kaplan

Şensoy

2022

Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence

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When collaborating with an artificial intelligence (AI) system, we need to assess when to trust its recommendations. Suppose we mistakenly trust it in regions where it is likely to err. In that case, catastrophic failures may occur, hence the need for Bayesian approaches for reasoning and learning to determine the confidence (or epistemic uncertainty) in the probabilities of the queried outcome. Pure Bayesian methods, however, suffer from high computational costs. To overcome them, we revert to efficient and effective approximations. In this paper, we focus on techniques that take the name of evidential reasoning and learning from the process of Bayesian update of given hypotheses based on additional evidence. This paper provides the reader with a gentle introduction to the area of investigation, the up-to-date research outcomes, and the open questions still left unanswered.

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“…Example 7. Consider the instance given in Table 6 [ Ghodsi et al, 2022]. It is not hard to check that the MMS values of the two agents are µ 2 1 = µ 2 2 = 1.…”

Section: General Valuationsmentioning

confidence: 99%

Fair Division of Indivisible Goods: A Survey

Amanatidis¹,

Birmpas²,

Filos-Ratsikas³

et al. 2022

Preprint

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Allocating resources to individuals in a fair manner has been a topic of interest since ancient times, with most of the early mathematical work on the problem focusing on resources that are infinitely divisible. Over the last decade, there has been a surge of papers studying computational questions regarding the indivisible case, for which exact fairness notions such as envy-freeness and proportionality are hard to satisfy. One main theme in the recent research agenda is to investigate the extent to which their relaxations, like maximin share fairness (MMS) and envy-freeness up to any good (EFX), can be achieved. In this survey, we present a comprehensive review of the progress made in the related literature by highlighting different ways to relax fairness notions, common algorithm design techniques, and the most interesting questions for future research.

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Fair allocation of indivisible goods: Beyond additive valuations

Cited by 13 publications

References 16 publications

Fair Allocation of Indivisible Chores: Beyond Additive Valuations

Fair Allocation of Indivisible Chores: Beyond Additive Valuations

Fair Division of Indivisible Goods: A Survey

Fair Division of Indivisible Goods: A Survey

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