241 research outputs found
Algorithms and complexity results for problems on fair division and imitation games
No full text"We study the problem of allocating indivisible goods to agents in a fair and efficient manner. We consider different notions of fairness such as envy-freeness up to one good (EF1) and envy-freeness up to any good (EFX) in conjuction with Pareto-optimality (PO). We present polynomial time algorithms for computing allocations that are EF1 and PO when (i) the number of agents is constant, and (ii) the number of different values that every agent has for the goods is constant. We also show that when there are exactly two values for the goods, an allocation that is EFX, PO and gives a 1.067-approximation to the Nash Social Welfare (NSW) can be computed in polynomial time. We also present algorithms that satisfy a different notions of fairness, like equitability up to one good (EQ1), and equitability up to any good (EQX) along with PO in some of these cases. On the complexity front, we show that the problem of computing EF1 and PO allocations belongs to class PLS. Further we show that deciding if EFX and PO allocations exist is NP-hard, even where there are at most two non-zero values for the goods.
We next consider the problem of computing the Nash Social Welfare maximizing allocation for the case of public goods subject to a cardinality constraint. We show that the NSW problem is NP-hard, even when the valuations are all binary. Next, we present a linear-factor approximation algorithm and polynomial time algorithms when the number of agents or the number of goods to be picked is constant. Finally we present NSW-preserving reductions from the model of private goods to that of public goods, and from the public goods model to that of public decision making, thus showing how the models are related.
Lastly, we study the problem of computing approximate Nash equilibria in imitation games. An imitation game is represented by two payoff matrices , in which is the identity matrix, implying that the second player gets a positive payoff only if she ``imitates"" the first. We show that much like the general case, for any , computing a -approximate NE of imitation games remains PPAD-hard, where is the number of moves available to the players. On the other hand, we design a polynomial-time algorithm to find -approximate NE for any given constant (PTAS). The former result also rules out the smooth complexity being in \Ptime, unless \PPAD \subset \RP."Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2022-08-01The student, Aniket Murhekar, accepted the attached license on 2020-07-17 at 20:25.The student, Aniket Murhekar, submitted this Thesis for approval on 2020-07-17 at 20:34.This Thesis was approved for publication on 2020-07-20 at 10:18.DSpace SAF Submission Ingestion Package generated from Vireo submission #15689 on 2020-10-02 at 15:51:47Made available in DSpace on 2020-10-07T22:50:05Z (GMT). No. of bitstreams: 2
MURHEKAR-THESIS-2020.pdf: 479836 bytes, checksum: 9b218fda07cba3a8d088ffdfa2255d91 (MD5)
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Previous issue date: 2020-07-20Embargo set by: Seth Robbins for item 116350
Lift date: 2022-10-07T22:50:13Z
Reason: Author requested closed access (OA after 2yrs) in Vireo ETD systemAuthor requested closed access (OA after 2yrs) in Vireo ETD systemLimite
Absence of Hemoglobinopathies and G6PD deficiency among the Jarawas, a primitive negretoid tribes of Andaman and Nicobar Islands
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MMWR. Morbidity and Mortality Weekly Report
No full textPain Awareness Month \u2014 September 2018Prevalence of Chronic Pain and High-Impact Chronic Pain Among Adults \u2014 United States, 2016 / James Dahlhamer, PhD; Jacqueline Lucas, MPH; Carla Zelaya, PhD; et al.Sexual Risk Behavior Differences Among Sexual Minority High School Students \u2014 United States, 2015 and 2017 / Catherine N. Rasberry, PhD; Richard Lowry, MD; Michelle Johns, PhD; et al.Sentinel Surveillance for Congenital Rubella Syndrome \u2014 India, 2016\u20132017 / Manoj Murhekar; Ashish Bavdekar; Asha Benakappa; et al.Notes from the Field: EnteroVirus A71 Neurologic Disease in Children \u2014 Colorado, 2018 / Kevin Messacar, MD; Alexis Burakoff, MD; W. Allan Nix; et al.Notes from the Field: Mumps Outbreak Associated with Cheerleading Competitions \u2014 North Texas, December 2016\u2013February 2017 / Diana Cervantes, DrPH; Heidi Honza, MPH; Daphne Lynch, MPH; et al.Erratum: Vol. 65, No. 15QuickStats: Age-Adjusted Death Rates for Lung Cancer, by Urbanization of County of Residence \u2014 National Vital Statistics System (U.S.), United States, 2006 and 2016
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