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Equitable Allocations of Indivisible Chores [article]

Rupert Freeman, Sujoy Sikdar, Rohit Vaish, Lirong Xia
2020 arXiv   pre-print
(Cited on page 4) Rupert Freeman, Sujoy Sikdar, Rohit Vaish, and Lirong Xia. Equitable Allocations of Indivisible Goods.  ... 
arXiv:2002.11504v1 fatcat:eyzwjfcbbjfvnfmtftpcgbt6pq

Matchings and Copeland's Method [article]

Telikepalli Kavitha, Rohit Vaish
2021 arXiv   pre-print
Given a graph G = (V,E) where every vertex has a weak ranking over its neighbors, we consider the problem of computing an optimal matching as per agent preferences. The classical notion of optimality in this setting is stability. However stable matchings, and more generally, popular matchings need not exist when G is non-bipartite. Unlike popular matchings, Copeland winners always exist in any voting instance – we study the complexity of computing a matching that is a Copeland winner and show
more » ... ere is no polynomial-time algorithm for this problem unless 𝖯 = 𝖭𝖯. We introduce a relaxation of both popular matchings and Copeland winners called weak Copeland winners. These are matchings with Copeland score at least μ/2, where μ is the total number of matchings in G; the maximum possible Copeland score is (μ-1/2). We show a fully polynomial-time randomized approximation scheme to compute a matching with Copeland score at least μ/2·(1-ε) for any ε > 0.
arXiv:2105.13729v2 fatcat:jrjrc4l4bveefmktrtsdmy2il4

Accomplice Manipulation of the Deferred Acceptance Algorithm [article]

Hadi Hosseini, Fatima Umar, Rohit Vaish
2020 arXiv   pre-print
(Cited on pages 1, 2, 3, and 9) Rohit Vaish and Dinesh Garg. Manipulating Gale-Shapley Algorithm: Preserving Stability and Remain- ing Inconspicuous.  ...  ., 2001; Kobayashi and Matsui, 2009, 2010; Vaish and Garg, 2017; Deng et al., 2018) .  ... 
arXiv:2012.04518v1 fatcat:v5j5jjbyonbvdodqzov6y564pa

Stable Fractional Matchings [article]

Ioannis Caragiannis, Aris Filos-Ratsikas, Panagiotis Kanellopoulos, Rohit Vaish
2020 arXiv   pre-print
Part of this work was done while Rohit Vaish was supported by the Prof. R Narasimhan postdoctoral award.  ...  Rohit Vaish acknowledges support from ONR#N00014-17-1-2621 while he was affiliated with Rensselaer Polytechnic Institute, and is currently supported by project no.  ... 
arXiv:1902.06698v2 fatcat:fodx5zag4fa6xe2bnq4sszemxy

Fair and Efficient Allocations under Lexicographic Preferences [article]

Hadi Hosseini, Sujoy Sikdar, Rohit Vaish, Lirong Xia
2020 arXiv   pre-print
Envy-freeness up to any good (EFX) provides a strong and intuitive guarantee of fairness in the allocation of indivisible goods. But whether such allocations always exist or whether they can be efficiently computed remains an important open question. We study the existence and computation of EFX in conjunction with various other economic properties under lexicographic preferences--a well-studied preference model in artificial intelligence and economics. In sharp contrast to the known results
more » ... additive valuations, we not only prove the existence of EFX and Pareto optimal allocations, but in fact provide an algorithmic characterization of these two properties. We also characterize the mechanisms that are, in addition, strategyproof, non-bossy, and neutral. When the efficiency notion is strengthened to rank-maximality, we obtain non-existence and computational hardness results, and show that tractability can be restored when EFX is relaxed to another well-studied fairness notion called maximin share guarantee (MMS).
arXiv:2012.07680v1 fatcat:hngw6rsx6rf5tmsroxl7qy76ym

Greedy Algorithms for Maximizing Nash Social Welfare [article]

Siddharth Barman, Sanath Kumar Krishnamurthy, Rohit Vaish
2018 arXiv   pre-print
We study the problem of fairly allocating a set of indivisible goods among agents with additive valuations. The extent of fairness of an allocation is measured by its Nash social welfare, which is the geometric mean of the valuations of the agents for their bundles. While the problem of maximizing Nash social welfare is known to be APX-hard in general, we study the effectiveness of simple, greedy algorithms in solving this problem in two interesting special cases. First, we show that a simple,
more » ... reedy algorithm provides a 1.061-approximation guarantee when agents have identical valuations, even though the problem of maximizing Nash social welfare remains NP-hard for this setting. Second, we show that when agents have binary valuations over the goods, an exact solution (i.e., a Nash optimal allocation) can be found in polynomial time via a greedy algorithm. Our results in the binary setting extend to provide novel, exact algorithms for optimizing Nash social welfare under concave valuations. Notably, for the above mentioned scenarios, our techniques provide a simple alternative to several of the existing, more sophisticated techniques for this problem such as constructing equilibria of Fisher markets or using real stable polynomials.
arXiv:1801.09046v1 fatcat:wkwvkarwrzhmfjbl7rhryb3fnu

Opting Into Optimal Matchings [article]

Avrim Blum, Ioannis Caragiannis, Nika Haghtalab, Ariel D. Procaccia, Eviatar B. Procaccia, Rohit Vaish
2016 arXiv   pre-print
We revisit the problem of designing optimal, individually rational matching mechanisms (in a general sense, allowing for cycles in directed graphs), where each player --- who is associated with a subset of vertices --- matches as many of his own vertices when he opts into the matching mechanism as when he opts out. We offer a new perspective on this problem by considering an arbitrary graph, but assuming that vertices are associated with players at random. Our main result asserts that, under
more » ... tain conditions, any fixed optimal matching is likely to be individually rational up to lower-order terms. We also show that a simple and practical mechanism is (fully) individually rational, and likely to be optimal up to lower-order terms. We discuss the implications of our results for market design in general, and kidney exchange in particular.
arXiv:1609.04051v1 fatcat:ox7zv53mlbabrbkv5f5mnmecq4

Finding Fair and Efficient Allocations [article]

Siddharth Barman, Sanath Kumar Krishnamurthy, Rohit Vaish
2018 arXiv   pre-print
We study the problem of allocating a set of indivisible goods among a set of agents in a fair and efficient manner. An allocation is said to be fair if it is envy-free up to one good (EF1), which means that each agent prefers its own bundle over the bundle of any other agent up to the removal of one good. In addition, an allocation is deemed efficient if it satisfies Pareto optimality (PO). While each of these well-studied properties is easy to achieve separately, achieving them together is far
more » ... from obvious. Recently, Caragiannis et al. (2016) established the surprising result that when agents have additive valuations for the goods, there always exists an allocation that simultaneously satisfies these two seemingly incompatible properties. Specifically, they showed that an allocation that maximizes the Nash social welfare (NSW) objective is both EF1 and PO. However, the problem of maximizing NSW is NP-hard. As a result, this approach does not provide an efficient algorithm for finding a fair and efficient allocation. In this paper, we bypass this barrier, and develop a pseudopolynomial time algorithm for finding allocations that are EF1 and PO; in particular, when the valuations are bounded, our algorithm finds such an allocation in polynomial time. Furthermore, we establish a stronger existence result compared to Caragiannis et al. (2016): For additive valuations, there always exists an allocation that is EF1 and fractionally PO. Another contribution of our work is to show that our algorithm provides a polynomial-time 1.45-approximation to the NSW objective. This improves upon the best known approximation ratio for this problem (namely, the 2-approximation algorithm of Cole et al. (2017)). Unlike many of the existing approaches, our algorithm is completely combinatorial.
arXiv:1707.04731v2 fatcat:ro5tbhuiwng7ro553pjrnl3a5a

Equitable Division of a Path [article]

Neeldhara Misra, Chinmay Sonar, P. R. Vaidyanathan, Rohit Vaish
2021 arXiv   pre-print
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
more » ... litarian welfare) is computationally hard even for binary additive valuations. On the algorithmic side, we show that by relaxing the efficiency requirement, a connected EQ1 allocation can be computed in polynomial time for any given ordering of agents, even for general monotone valuations. Interestingly, the allocation computed by our algorithm has the highest egalitarian welfare among all allocations consistent with the given ordering. On the other hand, if efficiency is required, then tractability can still be achieved for binary additive valuations with interval structure. On our way, we strengthen some of the existing results in the literature for other fairness notions such as envy-freeness up to one good (EF1), and also provide novel results for negatively-valued items or chores.
arXiv:2101.09794v2 fatcat:4zipwfiywff5dpzu26qga4s3ue

Fairly Dividing Mixtures of Goods and Chores under Lexicographic Preferences [article]

Hadi Hosseini, Sujoy Sikdar, Rohit Vaish, Lirong Xia
2022 arXiv   pre-print
Umang Bhaskar, AR Sricharan, and Rohit Vaish. On Approximate Envy-Freeness for Indivisible Chores and Mixed Resources.  ...  Siddharth Barman, Sanath Kumar Krishnamurthy, and Rohit Vaish. Finding Fair and Efficient Allocations. In EC, pages 557-574, 2018. Xiaohui Bei, University Press, 1996. Eric Budish.  ... 
arXiv:2203.07279v1 fatcat:oag446fydjhjtpro2ilbnslu74

Best of Both Worlds: Ex-Ante and Ex-Post Fairness in Resource Allocation [article]

Rupert Freeman, Nisarg Shah, Rohit Vaish
2020 arXiv   pre-print
We study the problem of allocating indivisible goods among agents with additive valuations. When randomization is allowed, it is possible to achieve compelling notions of fairness such as envy-freeness, which states that no agent should prefer any other agent's allocation to her own. When allocations must be deterministic, achieving exact fairness is impossible but approximate notions such as envy-freeness up to one good can be guaranteed. Our goal in this work is to achieve both
more » ... by constructing a randomized allocation that is exactly fair ex-ante and approximately fair ex-post. The key question we address is whether ex-ante envy-freeness can be achieved in combination with ex-post envy-freeness up to one good. We settle this positively by designing an efficient algorithm that achieves both properties simultaneously. If we additionally require economic efficiency, we obtain an impossibility result. However, we show that economic efficiency and ex-ante envy-freeness can be simultaneously achieved if we slightly relax our ex-post fairness guarantee. On our way, we characterize the well-known Maximum Nash Welfare allocation rule in terms of a recently introduced fairness guarantee that applies to groups of agents, not just individuals.
arXiv:2005.14122v1 fatcat:hk2hdzupfbaqpfn3arzbsqusuq

Fair Division through Information Withholding [article]

Hadi Hosseini, Sujoy Sikdar, Rohit Vaish, Jun Wang, Lirong Xia
2020 arXiv   pre-print
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
more » ... 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 close-to-optimal number of goods.
arXiv:1907.02583v3 fatcat:geuiytxucrdfddwdqyxqzb4bda

Manipulating Gale-Shapley Algorithm: Preserving Stability and Remaining Inconspicuous

Rohit Vaish, Dinesh Garg
2017 Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence  
We study the problem of manipulation of the men-proposing Gale-Shapley algorithm by a single woman via permutation of her true preference list. Our contribution is threefold: First, we show that the matching induced by an optimal manipulation is stable with respect to the true preferences. Second, we identify a class of optimal manipulations called inconspicuous manipulations which, in addition to preserving stability, are also nearly identical to the true preference list of the manipulator
more » ... ing the manipulation hard to be detected). Third, for optimal inconspicuous manipulations, we strengthen the stability result by showing that the entire stable lattice of the manipulated instance is contained inside the original lattice.​
doi:10.24963/ijcai.2017/62 dblp:conf/ijcai/VaishG17 fatcat:atnkcf6imnbs7jr7qynhvmpixi

Analysis and Prediction of COVID-19 Pandemic in India

Narayana Darapaneni, Praphul Jain, Rohit Khattar, Manish Chawla, Rijy Vaish, Anwesh Reddy Paduri
2020 2020 2nd International Conference on Advances in Computing, Communication Control and Networking (ICACCCN)  
In this paper, we have analysed the COVID-19 progression in India and the three most affected Indian states (viz. Maharashtra, Tamil Nadu and Andhra Pradesh) as of 29-Aug-20 and developed a prediction model to forecast the behaviour of COVID-19 spread in the future months. We used time series data for India and applied the Susceptible-Infective-Removed (SIR) model and the FbProphet model to predict the peak infectives and peak infective date for India and the three most affected states. In this
more » ... paper, we further performed the comparative analysis of the prediction results from SIR and FbProphet models. From this study, we concluded that with the assumption that a total 5% of India's population might be infected by the pandemic, the countrywide spread is forecasted to reach its peak by the end of Nov-20. And till the time there is no vaccination, for the states that have already reached their peak and with festivals around the corner, there are high chances of resurgence in the number of cases if the social distancing and other control measures are not followed diligently in the coming months.
doi:10.1109/icacccn51052.2020.9362817 fatcat:d6qelkkxtbauvlhuxl5e23xcfq

Fair Division Through Information Withholding

Hadi Hosseini, Sujoy Sikdar, Rohit Vaish, Hejun Wang, Lirong Xia
compare several known algorithms for computing EF1 allocations on synthetic and real-world preference data, and find that the round-robin algorithm and a recent algorithm of Barman, Krishnamurthy, and Vaish  ...  Fisher market-based algorithm (Alg-EF1+PO): This algorithm, due to Barman, Krishnamurthy, and Vaish (2018) , uses local search and price-rise subroutines in a Fisher market associated with the fair division  ... 
doi:10.1609/aaai.v34i02.5573 fatcat:d4kpll7l3bcw5k2hede5rje2ae
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