scholarly journals Equitable Allocations of Indivisible Goods

2019 ◽  
Author(s):  
Rupert Freeman ◽  
Sujoy Sikdar ◽  
Rohit Vaish ◽  
Lirong Xia
Keyword(s):  
Economic Efficiency ◽  
Pareto Optimality ◽  
Real World ◽  
Fair Division ◽  
Prior Work ◽  
Indivisible Goods ◽  
Preference Data ◽  
Novel Algorithm

In fair division, equitability dictates that each participant receives the same level of utility. In this work, we study equitable allocations of indivisible goods among agents with additive valuations. While prior work has studied (approximate) equitability in isolation, we consider equitability in conjunction with other well-studied notions of fairness and economic efficiency. We show that the Leximin algorithm produces an allocation that satisfies equitability up to any good and Pareto optimality. We also give a novel algorithm that guarantees Pareto optimality and equitability up to one good in pseudopolynomial time.  Our experiments on real-world preference data reveal that approximate envy-freeness, approximate equitability, and Pareto optimality can often be achieved simultaneously.

scholarly journals Fair Division Through Information Withholding

2020 ◽  
Vol 34 (02) ◽  
pp. 2014-2021
Author(s):  
Hadi Hosseini ◽  
Sujoy Sikdar ◽  
Rohit Vaish ◽  
Hejun Wang ◽  
Lirong Xia
Keyword(s):  
Real World ◽  
Fair Division ◽  
Optimal Number ◽  
The Other ◽  
Indivisible Goods ◽  
Worst Case ◽  
Optimal Amount ◽  
Preference Data ◽  
Amount Of Information ◽  
Information Withholding

Envy-freeness up to one good (EF1) is a well-studied fairness notion for indivisible goods that addresses pairwise envy by the removal of at most one good. In the worst case, each pair of agents might require the (hypothetical) removal of a different good, resulting in a weak aggregate guarantee. We study allocations that are nearly envy-free in aggregate, and define a novel fairness notion based on information withholding. Under this notion, an agent can withhold (or hide) some of the goods in its bundle and reveal the remaining goods to the other agents. We observe that in practice, envy-freeness can be achieved by withholding only a small number of goods overall. We show that finding allocations that withhold an optimal number of goods is computationally hard even for highly restricted classes of valuations. In contrast to the worst-case results, our experiments on synthetic and real-world preference data show that existing algorithms for finding EF1 allocations withhold a close-to-optimal amount of information.

scholarly journals On the Proximity of Markets with Integral Equilibria

2019 ◽  
Vol 33 ◽  
pp. 1748-1755 ◽  
Author(s):  
Siddharth Barman ◽  
Sanath Kumar Krishnamurthy
Keyword(s):  
Polynomial Time ◽  
Fair Division ◽  
Prior Work ◽  
Indivisible Goods ◽  
Polynomial Time Algorithms ◽  
Fairness And Efficiency ◽  
Pareto Efficient ◽  
Efficient Allocations ◽  
Strong Existence ◽  
Strongly Polynomial

We study Fisher markets that admit equilibria wherein each good is integrally assigned to some agent. While strong existence and computational guarantees are known for equilibria of Fisher markets with additive valuations (Eisenberg and Gale 1959; Orlin 2010), such equilibria, in general, assign goods fractionally to agents. Hence, Fisher markets are not directly applicable in the context of indivisible goods. In this work we show that one can always bypass this hurdle and, up to a bounded change in agents’ budgets, obtain markets that admit an integral equilibrium. We refer to such markets as pure markets and show that, for any given Fisher market (with additive valuations), one can efficiently compute a “near-by,” pure market with an accompanying integral equilibrium.Our work on pure markets leads to novel algorithmic results for fair division of indivisible goods. Prior work in discrete fair division has shown that, under additive valuations, there always exist allocations that simultaneously achieve the seemingly incompatible properties of fairness and efficiency (Caragiannis et al. 2016); here fairness refers to envyfreeness up to one good (EF1) and efficiency corresponds to Pareto efficiency. However, polynomial-time algorithms are not known for finding such allocations. Considering relaxations of proportionality and EF1, respectively, as our notions of fairness, we show that fair and Pareto efficient allocations can be computed in strongly polynomial time.

scholarly journals CIRO: The Effects of Visually Diminished Real Objects on Human Perception in Handheld Augmented Reality

Electronics ◽  
2021 ◽  
Vol 10 (8) ◽  
pp. 900
Author(s):  
Hanseob Kim ◽  
Taehyung Kim ◽  
Myungho Lee ◽  
Gerard Jounghyun Kim ◽  
Jae-In Hwang
Keyword(s):  
Augmented Reality ◽  
Real World ◽  
Human Perception ◽  
Ground Truth ◽  
Prior Work ◽  
Comparative Experiment ◽  
User Perception ◽  
Depth Distortion ◽  
Real Objects ◽  
Visual Artifacts

Augmented reality (AR) scenes often inadvertently contain real world objects that are not relevant to the main AR content, such as arbitrary passersby on the street. We refer to these real-world objects as content-irrelevant real objects (CIROs). CIROs may distract users from focusing on the AR content and bring about perceptual issues (e.g., depth distortion or physicality conflict). In a prior work, we carried out a comparative experiment investigating the effects on user perception of the AR content by the degree of the visual diminishment of such a CIRO. Our findings revealed that the diminished representation had positive impacts on human perception, such as reducing the distraction and increasing the presence of the AR objects in the real environment. However, in that work, the ground truth test was staged with perfect and artifact-free diminishment. In this work, we applied an actual real-time object diminishment algorithm on the handheld AR platform, which cannot be completely artifact-free in practice, and evaluated its performance both objectively and subjectively. We found that the imperfect diminishment and visual artifacts can negatively affect the subjective user experience.

An algorithm Walktrap-SPM for detecting overlapping community structure

2017 ◽  
Vol 31 (15) ◽  
pp. 1750121 ◽  
Author(s):  
Fang Hu ◽  
Youze Zhu ◽  
Yuan Shi ◽  
Jianchao Cai ◽  
Luogeng Chen ◽  
...  
Keyword(s):  
Community Structure ◽  
Random Walk ◽  
Community Detection ◽  
Real World ◽  
Overlapping Community Detection ◽  
Overlapping Communities ◽  
Running Time ◽  
Overlapping Community ◽  
Negative Links ◽  
Novel Algorithm

In this paper, based on Walktrap algorithm with the idea of random walk, and by selecting the neighbor communities, introducing improved signed probabilistic mixture (SPM) model and considering the edges within the community as positive links and the edges between the communities as negative links, a novel algorithm Walktrap-SPM for detecting overlapping community is proposed. This algorithm not only can identify the overlapping communities, but also can greatly increase the objectivity and accuracy of the results. In order to verify the accuracy, the performance of this algorithm is tested on several representative real-world networks and a set of computer-generated networks based on LFR benchmark. The experimental results indicate that this algorithm can identify the communities accurately, and it is more suitable for overlapping community detection. Compared with Walktrap, SPM and LMF algorithms, the presented algorithm can acquire higher values of modularity and NMI. Moreover, this new algorithm has faster running time than SPM and LMF algorithms.

scholarly journals Crawling the Community Structure of Multiplex Networks

2019 ◽  
Vol 33 ◽  
pp. 168-175 ◽  
Author(s):  
Ricky Laishram ◽  
Jeremy D. Wendt ◽  
Sucheta Soundarajan
Keyword(s):  
Community Structure ◽  
Real World ◽  
Multiplex Networks ◽  
Data Collector ◽  
Multiplex Network ◽  
Multiple Levels ◽  
Novel Algorithm ◽  
Collection Costs

We examine the problem of crawling the community structure of a multiplex network containing multiple layers of edge relationships. While there has been a great deal of work examining community structure in general, and some work on the problem of sampling a network to preserve its community structure, to the best of our knowledge, this is the first work to consider this problem on multiplex networks. We consider the specific case in which the layers of a multiplex network have different query (collection) costs and reliabilities; and a data collector is interested in identifying the community structure of the most expensive layer. We propose MultiComSample (MCS), a novel algorithm for crawling a multiplex network. MCS uses multiple levels of multi-armed bandits to determine the best layers, communities and node roles for selecting nodes to query. We test MCS against six baseline algorithms on real-world multiplex networks, and achieved large gains in performance. For example, after consuming a budget equivalent to sampling 20% of the nodes in the expensive layer, we observe that MCS outperforms the best baseline by up to 49%.

Combining Expert Strategies in Multimodal Classification

2014 ◽  
Vol 590 ◽  
pp. 693-697
Author(s):  
Jing Peng
Keyword(s):  
Real World ◽  
Classification Performance ◽  
Experimental Results ◽  
Robust Classification ◽  
Multimodal Classification ◽  
Novel Algorithm

In multimodal classification, we look for a set of strategies for mining and exploiting the most informative modalities for a given situation. These strategies are computations performed by the algorithms. In this paper, we propose to consider strategies as advice given to an algorithm by “expert.” There can be several classification strategies. Each strategy makes different assumptions regarding the fidelity of a sensor modality and uses different data to arrive at its estimates. Each strategy may place different trust in a sensor at different times, and each may be better in different situations. In this paper, we introduce a novel algorithm for combining expert strategies to achieve robust classification performance in a multimodal setting. We provide experimental results using real world examples to demonstrate the efficacy of the proposed algorithm.

scholarly journals Finding Fair and Efficient Allocations for Matroid Rank Valuations

2021 ◽  
Vol 9 (4) ◽  
pp. 1-41
Author(s):  
Nawal Benabbou ◽  
Mithun Chakraborty ◽  
Ayumi Igarashi ◽  
Yair Zick
Keyword(s):  
Convex Function ◽  
Real World ◽  
Function Class ◽  
Efficient Allocation ◽  
Indivisible Goods ◽  
Valuation Function ◽  
Bipartite Matching ◽  
Optimal Outcomes ◽  
Efficient Allocations ◽  
Rank Functions

In this article, we present new results on the fair and efficient allocation of indivisible goods to agents whose preferences correspond to matroid rank functions . This is a versatile valuation class with several desirable properties (such as monotonicity and submodularity), which naturally lends itself to a number of real-world domains. We use these properties to our advantage; first, we show that when agent valuations are matroid rank functions, a socially optimal (i.e., utilitarian social welfare-maximizing) allocation that achieves envy-freeness up to one item (EF1) exists and is computationally tractable. We also prove that the Nash welfare-maximizing and the leximin allocations both exhibit this fairness/efficiency combination by showing that they can be achieved by minimizing any symmetric strictly convex function over utilitarian optimal outcomes. To the best of our knowledge, this is the first valuation function class not subsumed by additive valuations for which it has been established that an allocation maximizing Nash welfare is EF1. Moreover, for a subclass of these valuation functions based on maximum (unweighted) bipartite matching, we show that a leximin allocation can be computed in polynomial time. Additionally, we explore possible extensions of our results to fairness criteria other than EF1 as well as to generalizations of the above valuation classes.

scholarly journals Fair Division with a Secretive Agent

2019 ◽  
Vol 33 ◽  
pp. 1732-1739
Author(s):  
Eshwar Ram Arunachaleswaran ◽  
Siddharth Barman ◽  
Nidhi Rathi
Keyword(s):  
Partial Information ◽  
Fair Division ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Indivisible Goods ◽  
Cake Cutting ◽  
Division Problems ◽  
Divisible Goods ◽  
Arbitrary Selection ◽  
Selection Of

We study classic fair-division problems in a partial information setting. This paper respectively addresses fair division of rent, cake, and indivisible goods among agents with cardinal preferences. We will show that, for all of these settings and under appropriate valuations, a fair (or an approximately fair) division among n agents can be efficiently computed using only the valuations of n − 1 agents. The nth (secretive) agent can make an arbitrary selection after the division has been proposed and, irrespective of her choice, the computed division will admit an overall fair allocation.For the rent-division setting we prove that well-behaved utilities of n − 1 agents suffice to find a rent division among n rooms such that, for every possible room selection of the secretive agent, there exists an allocation (of the remaining n − 1 rooms among the n − 1 agents) which ensures overall envy freeness (fairness). We complement this existential result by developing a polynomial-time algorithm for the case of quasilinear utilities. In this partial information setting, we also develop efficient algorithms to compute allocations that are envy-free up to one good (EF1) and ε-approximate envy free. These two notions of fairness are applicable in the context of indivisible goods and divisible goods (cake cutting), respectively.One of the main technical contributions of this paper is the development of novel connections between different fairdivision paradigms, e.g., we use our existential results for envy-free rent-division to develop an efficient EF1 algorithm.

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