scholarly journals The Fair Division of Hereditary Set Systems

2018 ◽  
pp. 297-311
Author(s):  
Z. Li ◽  
A. Vetta
Keyword(s):  
Fair Division ◽  
Set Systems

scholarly journals The Fair Division of Hereditary Set Systems

2021 ◽  
Vol 9 (2) ◽  
pp. 1-19
Author(s):  
Z. Li ◽  
A. Vetta
Keyword(s):  
Recent Work ◽  
Polynomial Time ◽  
Simple Algorithm ◽  
Fair Division ◽  
Set Systems

We consider the fair division of indivisible items using the maximin shares measure. Recent work on the topic has focused on extending results beyond the class of additive valuation functions. In this spirit, we study the case where the items form a hereditary set system. We present a simple algorithm that allocates each agent a bundle of items whose value is at least 0.3666 times the maximin share of the agent. This improves upon the current best known guarantee of 0.2 due to Ghodsi et al. The analysis of the algorithm is almost tight; we present an instance where the algorithm provides a guarantee of at most 0.3738. We also show that the algorithm can be implemented in polynomial time given a valuation oracle for each agent.

The Geometry of Efficient Fair Division

2005 ◽  
Author(s):  
Julius B. Barbanel ◽  
Alan D. Taylor
Keyword(s):  
Fair Division

Fair Division

2000 ◽  
Author(s):  
Michael J. Meurer
Keyword(s):  
Fair Division

scholarly journals Approximation Algorithms for Maximin Fair Division

2020 ◽  
Vol 8 (1) ◽  
pp. 1-28
Author(s):  
Siddharth Barman ◽  
Sanath Kumar Krishnamurthy
Keyword(s):  
Approximation Algorithms ◽  
Fair Division

scholarly journals Unavoidable subprojections in union-closed set systems of infinite breadth

2021 ◽  
Vol 94 ◽  
pp. 103311
Author(s):  
Yemon Choi ◽  
Mahya Ghandehari ◽  
Hung Le Pham
Keyword(s):  
Closed Set ◽  
Set Systems

scholarly journals Maternal mental health and well-being during the COVID-19 pandemic in Beijing, China

2021 ◽  
Author(s):  
Zhuang Wei ◽  
Ming-Yue Gao ◽  
Mary Fewtrell ◽  
Jonathan Wells ◽  
Jin-Yue Yu
Keyword(s):  
Mental Health ◽  
Higher Education ◽  
Maternal Mental Health ◽  
Descriptive Analysis ◽  
Fair Division ◽  
Personal Space ◽  
Well Being ◽  
Maternal Characteristics ◽  
The Impact ◽  
Beijing China

Abstract Background The aim of this study is to evaluate the impact of the coronavirus disease 2019 (COVID-19) pandemic on breastfeeding women and to identify predictors of maternal mental health and coping. Methods Mothers aged ≥ 18 years with a breast-fed infant ≤ 18 months of age during the COVID-19 pandemic in Beijing, China, completed a questionnaire. Descriptive analysis of lockdown consequences was performed and predictors of these outcomes were examined using stepwise linear regression. Results Of 2233 participants, 29.9%, 20.0% and 34.7% felt down, lonely, and worried, respectively, during the lockdown; however, 85.3% felt able to cope. Poorer maternal mental health was predicted by maternal (younger age, higher education) and infant (older age, lower gestation) characteristics, and social circumstances (husband unemployed or working from home, receiving advice from family, having enough space for the baby, living close to a park or green space). Conversely, better maternal mental health was predicted by higher income, employment requiring higher qualifications, more personal space at home, shopping or walking > once/week and lack of impact of COVID-19 on job or income. Mothers with higher education, more bedrooms, fair division of household chores and attending an online mother and baby group > once/week reported better coping. Conclusion The findings highlight maternal characteristics and circumstances that predict poorer mental health and reduced coping which could be used to target interventions in any future public health emergencies requiring social restrictions.

scholarly journals The VC Dimension of Metric Balls under Fréchet and Hausdorff Distances

2021 ◽  
Author(s):  
Anne Driemel ◽  
André Nusser ◽  
Jeff M. Phillips ◽  
Ioannis Psarros
Keyword(s):  
Density Estimation ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Similarity Metrics ◽  
Vc Dimension ◽  
Set Systems ◽  
Polygonal Curves ◽  
The Individual ◽  
Curve Similarity ◽  
Metric Balls

AbstractThe Vapnik–Chervonenkis dimension provides a notion of complexity for systems of sets. If the VC dimension is small, then knowing this can drastically simplify fundamental computational tasks such as classification, range counting, and density estimation through the use of sampling bounds. We analyze set systems where the ground set X is a set of polygonal curves in $$\mathbb {R}^d$$ R d and the sets $$\mathcal {R}$$ R are metric balls defined by curve similarity metrics, such as the Fréchet distance and the Hausdorff distance, as well as their discrete counterparts. We derive upper and lower bounds on the VC dimension that imply useful sampling bounds in the setting that the number of curves is large, but the complexity of the individual curves is small. Our upper and lower bounds are either near-quadratic or near-linear in the complexity of the curves that define the ranges and they are logarithmic in the complexity of the curves that define the ground set.

scholarly journals Truthful fair division without free disposal

2020 ◽  
Vol 55 (3) ◽  
pp. 523-545 ◽  
Author(s):  
Xiaohui Bei ◽  
Guangda Huzhang ◽  
Warut Suksompong
Keyword(s):  
Fair Division ◽  
Multiple Agents ◽  
Two Agents ◽  
Free Disposal ◽  
Cake Cutting ◽  
Strategic Agents ◽  
Additional Constraints

Abstract We study the problem of fairly dividing a heterogeneous resource, commonly known as cake cutting and chore division, in the presence of strategic agents. While a number of results in this setting have been established in previous works, they rely crucially on the free disposal assumption, meaning that the mechanism is allowed to throw away part of the resource at no cost. In the present work, we remove this assumption and focus on mechanisms that always allocate the entire resource. We exhibit a truthful and envy-free mechanism for cake cutting and chore division for two agents with piecewise uniform valuations, and we complement our result by showing that such a mechanism does not exist when certain additional constraints are imposed on the mechanisms. Moreover, we provide bounds on the efficiency of mechanisms satisfying various properties, and give truthful mechanisms for multiple agents with restricted classes of valuations.

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