Aravind Srinivasan

Brian Brubach, Nathaniel Grammel, Will Ma et al.

Matching is one of the most fundamental and broadly applicable problems across many domains. In these diverse real-world applications, there is often a degree of uncertainty in the input which has led to the study of stochastic matching models. Here, each edge in the graph has a known, independent probability of existing derived from some prediction. Algorithms must probe edges to determine existence and match them irrevocably if they exist. Further, each vertex may have a patience constraint denoting how many of its neighboring edges can be probed. We present new ordered contention resolution schemes yielding improved approximation guarantees for some of the foundational problems studied in this area. For stochastic matching with patience constraints in general graphs, we provide a 0.382-approximate algorithm assuming each vertex has patience at least $2$. Under this assumption, we improve upon the previous best 0.31-approximation of Baveja et al. (2018). When the vertices do not have patience constraints, we describe a 0.432-approximate random order probing algorithm with several corollaries such as an improved guarantee for the Prophet Secretary problem under Edge Arrivals. Finally, for the special case of bipartite graphs with unit patience constraints on one of the partitions, we show a 0.632-approximate algorithm that improves on the recent $1/3$-guarantee of Hikima et al. (2021).

Amy Babay, Michael Dinitz, Aravind Srinivasan et al.

The spread of an epidemic is often modeled by an SIR random process on a social network graph. The MinINF problem for optimal social distancing involves minimizing the expected number of infections, when we are allowed to break at most $B$ edges; similarly the MinINFNode problem involves removing at most $B$ vertices. These are fundamental problems in epidemiology and network science. While a number of heuristics have been considered, the complexity of these problems remains generally open. In this paper, we present two bicriteria approximation algorithms for MinINF, which give the first non-trivial approximations for this problem. The first is based on the cut sparsification result of Karger \cite{karger:mathor99}, and works when the transmission probabilities are not too small. The second is a Sample Average Approximation (SAA) based algorithm, which we analyze for the Chung-Lu random graph model. We also extend some of our results to tackle the MinINFNode problem.

George Li, Ann Li, Madhav Marathe et al.

In response to COVID-19, many countries have mandated social distancing and banned large group gatherings in order to slow down the spread of SARS-CoV-2. These social interventions along with vaccines remain the best way forward to reduce the spread of SARS CoV-2. In order to increase vaccine accessibility, states such as Virginia have deployed mobile vaccination centers to distribute vaccines across the state. When choosing where to place these sites, there are two important factors to take into account: accessibility and equity. We formulate a combinatorial problem that captures these factors and then develop efficient algorithms with theoretical guarantees on both of these aspects. Furthermore, we study the inherent hardness of the problem, and demonstrate strong impossibility results. Finally, we run computational experiments on real-world data to show the efficacy of our methods.

Seyed A. Esmaeili, Sharmila Duppala, Davidson Cheng et al.

Online bipartite-matching platforms are ubiquitous and find applications in important areas such as crowdsourcing and ridesharing. In the most general form, the platform consists of three entities: two sides to be matched and a platform operator that decides the matching. The design of algorithms for such platforms has traditionally focused on the operator's (expected) profit. Since fairness has become an important consideration that was ignored in the existing algorithms a collection of online matching algorithms have been developed that give a fair treatment guarantee for one side of the market at the expense of a drop in the operator's profit. In this paper, we generalize the existing work to offer fair treatment guarantees to both sides of the market simultaneously, at a calculated worst case drop to operator profit. We consider group and individual Rawlsian fairness criteria. Moreover, our algorithms have theoretical guarantees and have adjustable parameters that can be tuned as desired to balance the trade-off between the utilities of the three sides. We also derive hardness results that give clear upper bounds over the performance of any algorithm.

Christine Herlihy, Aviva Prins, Aravind Srinivasan et al.

Restless and collapsing bandits are often used to model budget-constrained resource allocation in settings where arms have action-dependent transition probabilities, such as the allocation of health interventions among patients. However, state-of-the-art Whittle-index-based approaches to this planning problem either do not consider fairness among arms, or incentivize fairness without guaranteeing it. We thus introduce ProbFair, a probabilistically fair policy that maximizes total expected reward and satisfies the budget constraint while ensuring a strictly positive lower bound on the probability of being pulled at each timestep. We evaluate our algorithm on a real-world application, where interventions support continuous positive airway pressure (CPAP) therapy adherence among patients, as well as on a broader class of synthetic transition matrices. We find that ProbFair preserves utility while providing fairness guarantees.

Seyed A. Esmaeili, Brian Brubach, Aravind Srinivasan et al.

Clustering is a fundamental unsupervised learning problem where a dataset is partitioned into clusters that consist of nearby points in a metric space. A recent variant, fair clustering, associates a color with each point representing its group membership and requires that each color has (approximately) equal representation in each cluster to satisfy group fairness. In this model, the cost of the clustering objective increases due to enforcing fairness in the algorithm. The relative increase in the cost, the ''price of fairness,'' can indeed be unbounded. Therefore, in this paper we propose to treat an upper bound on the clustering objective as a constraint on the clustering problem, and to maximize equality of representation subject to it. We consider two fairness objectives: the group utilitarian objective and the group egalitarian objective, as well as the group leximin objective which generalizes the group egalitarian objective. We derive fundamental lower bounds on the approximation of the utilitarian and egalitarian objectives and introduce algorithms with provable guarantees for them. For the leximin objective we introduce an effective heuristic algorithm. We further derive impossibility results for other natural fairness objectives. We conclude with experimental results on real-world datasets that demonstrate the validity of our algorithms.

Michael Dinitz, Aravind Srinivasan, Leonidas Tsepenekas et al.

Graph cut problems are fundamental in Combinatorial Optimization, and are a central object of study in both theory and practice. Furthermore, the study of \emph{fairness} in Algorithmic Design and Machine Learning has recently received significant attention, with many different notions proposed and analyzed for a variety of contexts. In this paper we initiate the study of fairness for graph cut problems by giving the first fair definitions for them, and subsequently we demonstrate appropriate algorithmic techniques that yield a rigorous theoretical analysis. Specifically, we incorporate two different notions of fairness, namely \emph{demographic} and \emph{probabilistic individual} fairness, in a particular cut problem that models disaster containment scenarios. Our results include a variety of approximation algorithms with provable theoretical guarantees.

Darshan Chakrabarti, John P. Dickerson, Seyed A. Esmaeili et al.

Clustering is a fundamental problem in unsupervised machine learning, and fair variants of it have recently received significant attention due to its societal implications. In this work we introduce a novel definition of individual fairness for clustering problems. Specifically, in our model, each point $j$ has a set of other points $\mathcal{S}_j$ that it perceives as similar to itself, and it feels that it is fairly treated if the quality of service it receives in the solution is $α$-close (in a multiplicative sense, for a given $α\geq 1$) to that of the points in $\mathcal{S}_j$. We begin our study by answering questions regarding the structure of the problem, namely for what values of $α$ the problem is well-defined, and what the behavior of the \emph{Price of Fairness (PoF)} for it is. For the well-defined region of $α$, we provide efficient and easily-implementable approximation algorithms for the $k$-center objective, which in certain cases enjoy bounded-PoF guarantees. We finally complement our analysis by an extensive suite of experiments that validates the effectiveness of our theoretical results.

Brian Brubach, Darshan Chakrabarti, John P. Dickerson et al.

Metric clustering is fundamental in areas ranging from Combinatorial Optimization and Data Mining, to Machine Learning and Operations Research. However, in a variety of situations we may have additional requirements or knowledge, distinct from the underlying metric, regarding which pairs of points should be clustered together. To capture and analyze such scenarios, we introduce a novel family of \emph{stochastic pairwise constraints}, which we incorporate into several essential clustering objectives (radius/median/means). Moreover, we demonstrate that these constraints can succinctly model an intriguing collection of applications, including among others \emph{Individual Fairness} in clustering and \emph{Must-link} constraints in semi-supervised learning. Our main result consists of a general framework that yields approximation algorithms with provable guarantees for important clustering objectives, while at the same time producing solutions that respect the stochastic pairwise constraints. Furthermore, for certain objectives we devise improved results in the case of Must-link constraints, which are also the best possible from a theoretical perspective. Finally, we present experimental evidence that validates the effectiveness of our algorithms.

Brian Brubach, Darshan Chakrabarti, John P. Dickerson et al.

Clustering is a foundational problem in machine learning with numerous applications. As machine learning increases in ubiquity as a backend for automated systems, concerns about fairness arise. Much of the current literature on fairness deals with discrimination against protected classes in supervised learning (group fairness). We define a different notion of fair clustering wherein the probability that two points (or a community of points) become separated is bounded by an increasing function of their pairwise distance (or community diameter). We capture the situation where data points represent people who gain some benefit from being clustered together. Unfairness arises when certain points are deterministically separated, either arbitrarily or by someone who intends to harm them as in the case of gerrymandering election districts. In response, we formally define two new types of fairness in the clustering setting, pairwise fairness and community preservation. To explore the practicality of our fairness goals, we devise an approach for extending existing $k$-center algorithms to satisfy these fairness constraints. Analysis of this approach proves that reasonable approximations can be achieved while maintaining fairness. In experiments, we compare the effectiveness of our approach to classical $k$-center algorithms/heuristics and explore the tradeoff between optimal clustering and fairness.

Vedant Nanda, Pan Xu, Karthik Abinav Sankararaman et al.

Rideshare platforms, when assigning requests to drivers, tend to maximize profit for the system and/or minimize waiting time for riders. Such platforms can exacerbate biases that drivers may have over certain types of requests. We consider the case of peak hours when the demand for rides is more than the supply of drivers. Drivers are well aware of their advantage during the peak hours and can choose to be selective about which rides to accept. Moreover, if in such a scenario, the assignment of requests to drivers (by the platform) is made only to maximize profit and/or minimize wait time for riders, requests of a certain type (e.g. from a non-popular pickup location, or to a non-popular drop-off location) might never be assigned to a driver. Such a system can be highly unfair to riders. However, increasing fairness might come at a cost of the overall profit made by the rideshare platform. To balance these conflicting goals, we present a flexible, non-adaptive algorithm, \lpalg, that allows the platform designer to control the profit and fairness of the system via parameters $α$ and $β$ respectively. We model the matching problem as an online bipartite matching where the set of drivers is offline and requests arrive online. Upon the arrival of a request, we use \lpalg to assign it to a driver (the driver might then choose to accept or reject it) or reject the request. We formalize the measures of profit and fairness in our setting and show that by using \lpalg, the competitive ratios for profit and fairness measures would be no worse than $α/e$ and $β/e$ respectively. Extensive experimental results on both real-world and synthetic datasets confirm the validity of our theoretical lower bounds. Additionally, they show that $\lpalg$ under some choice of $(α, β)$ can beat two natural heuristics, Greedy and Uniform, on \emph{both} fairness and profit.

Michael J. Curry, John P. Dickerson, Karthik Abinav Sankararaman et al.

Rideshare platforms such as Uber and Lyft dynamically dispatch drivers to match riders' requests. We model the dispatching process in rideshare as a Markov chain that takes into account the geographic mobility of both drivers and riders over time. Prior work explores dispatch policies in the limit of such Markov chains; we characterize when this limit assumption is valid, under a variety of natural dispatch policies. We give explicit bounds on convergence in general, and exact (including constants) convergence rates for special cases. Then, on simulated and real transit data, we show that our bounds characterize convergence rates -- even when the necessary theoretical assumptions are relaxed. Additionally these policies compare well against a standard reinforcement learning algorithm which optimizes for profit without any convergence properties.

Brian Brubach, Karthik Abinav Sankararaman, Aravind Srinivasan et al.

Online matching problems have garnered significant attention in recent years due to numerous applications in e-commerce, online advertisements, ride-sharing, etc. Many of them capture the uncertainty in the real world by including stochasticity in both the arrival process and the matching process. The Online Stochastic Matching with Timeouts problem introduced by Bansal, et al., (Algorithmica, 2012) models matching markets (e.g., E-Bay, Amazon). Buyers arrive from an independent and identically distributed (i.i.d.) known distribution on buyer profiles and can be shown a list of items one at a time. Each buyer has some probability of purchasing each item and a limit (timeout) on the number of items they can be shown. Bansal et al., (Algorithmica, 2012) gave a 0.12-competitive algorithm which was improved by Adamczyk, et al., (ESA, 2015) to 0.24. We present an online attenuation framework that uses an algorithm for offline stochastic matching as a black box. On the upper bound side, we show that this framework, combined with a black-box adapted from Bansal et al., (Algorithmica, 2012), yields an online algorithm which nearly doubles the ratio to 0.46. On the lower bound side, we show that no algorithm can achieve a ratio better than 0.632 using the standard LP for this problem. This framework has a high potential for further improvements since new algorithms for offline stochastic matching can directly improve the ratio for the online problem. Our online framework also has the potential for a variety of extensions. For example, we introduce a natural generalization: Online Stochastic Matching with Two-sided Timeouts in which both online and offline vertices have timeouts. Our framework provides the first algorithm for this problem achieving a ratio of 0.30. We once again use the algorithm of Adamczyk et al., (ESA, 2015) as a black-box and plug-it into our framework.

John P Dickerson, Karthik A Sankararaman, Aravind Srinivasan et al.

Bipartite matching markets pair agents on one side of a market with agents, items, or contracts on the opposing side. Prior work addresses online bipartite matching markets, where agents arrive over time and are dynamically matched to a known set of disposable resources. In this paper, we propose a new model, Online Matching with (offline) Reusable Resources under Known Adversarial Distributions (OM-RR-KAD), in which resources on the offline side are reusable instead of disposable; that is, once matched, resources become available again at some point in the future. We show that our model is tractable by presenting an LP-based adaptive algorithm that achieves an online competitive ratio of 1/2 - eps for any given eps greater than 0. We also show that no non-adaptive algorithm can achieve a ratio of 1/2 + o(1) based on the same benchmark LP. Through a data-driven analysis on a massive openly-available dataset, we show our model is robust enough to capture the application of taxi dispatching services and ride-sharing systems. We also present heuristics that perform well in practice.