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In this paper we develop a procedure to deal with a family of parameter-dependent ill-posed problems, for which the exact solution in general does not exist. The original problems are relaxed by considering corresponding approximate ones,…
House Allocations concern with matchings involving one-sided preferences, where houses serve as a proxy encoding valuable indivisible resources (e.g. organs, course seats, subsidized public housing units) to be allocated among the agents.…
We describe a parallel approximation algorithm for maximizing monotone submodular functions subject to hereditary constraints on distributed memory multiprocessors. Our work is motivated by the need to solve submodular optimization problems…
A major problem in data augmentation is to ensure that the generated new samples cover the search space. This is a challenging problem and requires exploration for data augmentation policies to ensure their effectiveness in covering the…
Ranking algorithms are deployed widely to order a set of items in applications such as search engines, news feeds, and recommendation systems. Recent studies, however, have shown that, left unchecked, the output of ranking algorithms can…
Multiobjective combinatorial optimization deals with problems considering more than one viewpoint or scenario. The problem of aggregating multiple criteria to obtain a globalizing objective function is of special interest when the number of…
Motivated by the dynamic assortment offerings and item pricings occurring in e-commerce, we study a general problem of allocating finite inventories to heterogeneous customers arriving sequentially. We analyze this problem under the…
We study resource allocation in two-sided markets from a fundamental perspective and introduce a general modeling and algorithmic framework to effectively incorporate the complex and multidimensional aspects of fairness. Our main technical…
We study the problem of approximate social welfare maximization (without money) in one-sided matching problems when agents have unrestricted cardinal preferences over a finite set of items. Random priority is a very well-known…
We provide theoretical bounds on the worst case performance of the greedy algorithm in seeking to maximize a normalized, monotone, but not necessarily submodular objective function under a simple partition matroid constraint. We also…
Online bipartite matching with edge arrivals remained a major open question for a long time until a recent negative result by [Gamlath et al. FOCS 2019], who showed that no online policy is better than the straightforward greedy algorithm,…
We study the average performance of online greedy matching algorithms on $G(n,n,p)$, the random bipartite graph with $n$ vertices on each side and edges occurring independently with probability $p=p(n)$. In the online model, vertices on one…
Ensuring artificial intelligence behaves in such a way that is aligned with human values is commonly referred to as the alignment challenge. Prior work has shown that rational agents, behaving in such a way that maximizes a utility…
We outline a new approach for solving optimization problems which enforce triangle inequalities on output variables. We refer to this as metric-constrained optimization, and give several examples where problems of this form arise in machine…
In this paper, we study the problem of {\em $k$-center clustering with outliers}. The problem has many important applications in real world, but the presence of outliers can significantly increase the computational complexity. Though a…
We generalize the problem of online submodular welfare maximization to incorporate various stochastic elements that have gained significant attention in recent years. We show that a non-adaptive Greedy algorithm, which is oblivious to the…
We study the problem of assigning robots with actions to track targets. The objective is to optimize the robot team's tracking quality which can be defined as the reduction in the uncertainty of the targets' states. Specifically, we…
Most prior work on online matching problems has been with the flexibility of keeping some vertices unmatched. We study three related online matching problems with the constraint of matching every vertex, i.e., with no rejections. We adopt a…
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…
In this paper, we study the non-monotone adaptive submodular maximization problem subject to a cardinality constraint. We first revisit the adaptive random greedy algorithm proposed in \citep{gotovos2015non}, where they show that this…