skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


Title: Fair Stable Matching Meets Correlated Preferences
Stable matching models are widely used in market design, school admission, and donor organ exchange. The classic Deferred Acceptance (DA) algorithm guarantees a stable matching that is optimal for one side (say men) and pessimal for the other (say women). A sex-equal stable matching aims at providing a fair solution to this problem. We demonstrate that under a class of correlated preferences, the DA algorithm either returns a sex-equal solution or has a very low sex-equality cost.  more » « less
Award ID(s):
2052488 1850076 2107173
PAR ID:
10353559
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Proceedings of the 21st International Conference on Autonomous Agents and Multiagent Systems
Page Range / eLocation ID:
190-198
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. While the stable marriage problem and its variants model a vast range of matching markets, they fail to capture complex agent relationships, such as the affiliation of applicants and employers in an interview marketplace. To model this problem, the existing literature on matching with externalities permits agents to provide complete and total rankings over matchings based off of both their own and their affiliates' matches. This complete ordering restriction is unrealistic, and further the model may have an empty core. To address this, we introduce the Dichotomous Affiliate Stable Matching (DASM) Problem, where agents' preferences indicate dichotomous acceptance or rejection of another agent in the marketplace, both for themselves and their affiliates. We also assume the agent's preferences over entire matchings are determined by a general weighted valuation function of their (and their affiliates') matches. Our results are threefold: (1) we use a human study to show that real-world matching rankings follow our assumed valuation function; (2) we prove that there always exists a stable solution by providing an efficient, easily-implementable algorithm that finds such a solution; and (3) we experimentally validate the efficiency of our algorithm versus a linear-programming-based approach. 
    more » « less
  2. Domain adaptation (DA) addresses the real-world image classification problem of discrepancy between training (source) and testing (target) data distributions. We propose an unsupervised DA method that considers the presence of only unlabelled data in the target do- main. Our approach centers on finding matches between samples of the source and target domains. The matches are obtained by treating the source and target domains as hyper-graphs and carrying out a class-regularized hyper-graph matching using first-, second- and third-order similarities between the graphs. We have also developed a computationally efficient algorithm by initially selecting a subset of the samples to construct a graph and then developing a customized optimization routine for graph-matching based on Conditional Gradient and Alternating Direction Multiplier Method. This allows the proposed method to be used widely. We also performed a set of experiments on standard object recognition datasets to validate the effectiveness of our framework over previous approaches. 
    more » « less
  3. We study the classic Maximum Independent Set problem under the notion of stability introduced by Bilu and Linial (2010): a weighted instance of Independent Set is γ-stable if it has a unique optimal solution that remains the unique optimal solution under multiplicative perturbations of the weights by a factor of at most γ ≥ 1. The goal then is to efficiently recover this “pronounced” optimal solution exactly. In this work, we solve stable instances of Independent Set on several classes of graphs: we improve upon previous results by solving \tilde{O}(∆/sqrt(log ∆))-stable instances on graphs of maximum degree ∆, (k − 1)-stable instances on k-colorable graphs and (1 + ε)-stable instances on planar graphs (for any fixed ε > 0), using both combinatorial techniques as well as LPs and the Sherali-Adams hierarchy. For general graphs, we give an algorithm for (εn)-stable instances, for any fixed ε > 0, and lower bounds based on the planted clique conjecture. As a by-product of our techniques, we give algorithms as well as lower bounds for stable instances of Node Multiway Cut (a generalization of Edge Multiway Cut), by exploiting its connections to Vertex Cover. Furthermore, we prove a general structural result showing that the integrality gap of convex relaxations of several maximization problems reduces dramatically on stable instances. Moreover, we initiate the study of certified algorithms for Independent Set. The notion of a γ-certified algorithm was introduced very recently by Makarychev and Makarychev (2018) and it is a class of γ-approximation algorithms that satisfy one crucial property: the solution returned is optimal for a perturbation of the original instance, where perturbations are again multiplicative up to a factor of γ ≥ 1 (hence, such algorithms not only solve γ-stable instances optimally, but also have guarantees even on unstable instances). Here, we obtain ∆-certified algorithms for Independent Set on graphs of maximum degree ∆, and (1 + ε)-certified algorithms on planar graphs. Finally, we analyze the algorithm of Berman and Fürer (1994) and prove that it is a ((∆+1)/3 + ε)-certified algorithm for Independent Set on graphs of maximum degree ∆ where all weights are equal to 1. 
    more » « less
  4. The excitatory neurotoxin domoic acid (DA) consistently contaminates food webs in coastal regions around the world. Acute exposure to the toxin causes Amnesic Shellfish Poisoning, a potentially lethal syndrome of gastrointestinal- and seizure-related outcomes. Both advanced age and male sex have been suggested to contribute to interindividual DA susceptibility. To test this, we administered DA doses between 0.5 and 2.5 mg/kg body weight to female and male C57Bl/6 mice at adult (7–9-month-old) and aged (25–28-month-old) life stages and observed seizure-related activity for 90 min, at which point we euthanized the mice and collected serum, cortical, and kidney samples. We observed severe clonic–tonic convulsions in some aged individuals, but not in younger adults. We also saw an association between advanced age and the incidence of a moderately severe seizure-related outcome, hindlimb tremors, and between advanced age and overall symptom severity and persistence. Surprisingly, we additionally report that female mice, particularly aged female mice, demonstrated more severe neurotoxic symptoms following acute exposure to DA than males. Both age and sex patterns were reflected in tissue DA concentrations as well: aged mice and females had generally higher concentrations of DA in their tissues at 90 min post-exposure. This study contributes to the body of work that can inform intelligent, evidence-based public health protections for communities threatened by more frequent and extensive DA-producing algal blooms. 
    more » « less
  5. Dopamine (DA) is an important neurotransmitter, which is essential for transmitting signals in neuronal communications. The deficiency of DA release from neurons is implicated in neurological disorders. There has been great interest in developing new optical probes for monitoring the release behavior of DA from neurons. H-aggregates of organic dyes represent an ordered supramolecular structure with delocalized excitons. In this paper, we use the self-assembly of 3,3′-diethylthiadicarbocyanine iodide (DiSC 2 (5)) in ammonia solution to develop crystalline H-aggregate nanoparticles, in which DiSC 2 (5) molecules show long-range π–π stacking. The crystalline H-aggregate nanoparticles are stable in cell culture medium and can serve as an efficient photo-induced electron transfer (PET) probe for the detection of DA with the concentration as low as 0.1 nM in cell culture medium. Furthermore, the crystalline H-aggregate nanoparticle-based PET probe is used to detect the release behavior of DA from the M17 human neuroblastoma cells. We find that the DA release from the cells is enhanced by nicotine stimulations. Our results highlight the potential of crystalline H-aggregate nanoparticle-based PET probes for diagnosing nervous system diseases and verifying therapies. 
    more » « less