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Submodular maximization subject to matroid constraints is a central problem with many applications in machine learning. As algorithms are increasingly used in decision-making over datapoints with sensitive attributes such as gender or race,…
In this work we present the first practical $\left(\frac{1}{e}-\epsilon\right)$-approximation algorithm to maximise a general non-negative submodular function subject to a matroid constraint. Our algorithm is based on combining the…
We consider fast algorithms for monotone submodular maximization with a general matroid constraint. We present a randomized $(1 - 1/e - \epsilon)$-approximation algorithm that requires $\tilde{O}_{\epsilon}(\sqrt{r} n)$ independence oracle…
The maximization of submodular functions have found widespread application in areas such as machine learning, combinatorial optimization, and economics, where practitioners often wish to enforce various constraints; the matroid constraint…
A matroid is a notion of independence in combinatorial optimization which is closely related to computational efficiency. In particular, it is well known that the maximum of a constrained modular function can be found greedily if and only…
Finding diverse solutions to optimization problems has been of practical interest for several decades, and recently enjoyed increasing attention in research. While submodular optimization has been rigorously studied in many fields, its…
We study the online submodular maximization problem with free disposal under a matroid constraint. Elements from some ground set arrive one by one in rounds, and the algorithm maintains a feasible set that is independent in the underlying…
In this paper, we apply a Threshold-Decreasing Algorithm to maximize $k$-submodular functions under a matroid constraint, which reduces the query complexity of the algorithm compared to the greedy algorithm with little loss in approximation…
We present an optimal, combinatorial 1-1/e approximation algorithm for monotone submodular optimization over a matroid constraint. Compared to the continuous greedy algorithm (Calinescu, Chekuri, Pal and Vondrak, 2008), our algorithm is…
Constrained submodular maximization problems have long been studied, with near-optimal results known under a variety of constraints when the submodular function is monotone. The case of non-monotone submodular maximization is less…
We consider the problem of maximizing a nonnegative (possibly non-monotone) submodular set function with or without constraints. Feige et al. [FOCS'07] showed a 2/5-approximation for the unconstrained problem and also proved that no…
Constrained maximization of submodular functions poses a central problem in combinatorial optimization. In many realistic scenarios, a number of agents need to maximize multiple submodular objectives over the same ground set. We study such…
Submodular maximization under matroid and cardinality constraints are classical problems with a wide range of applications in machine learning, auction theory, and combinatorial optimization. In this paper, we consider these problems in the…
In this work, we consider robust submodular maximization with matroid constraints. We give an efficient bi-criteria approximation algorithm that outputs a small family of feasible sets whose union has (nearly) optimal objective value. This…
Submodular maximization over a matroid constraint is a fundamental problem with various applications in machine learning. Some of these applications involve decision-making over datapoints with sensitive attributes such as gender or race.…
Maximizing monotone submodular functions under a matroid constraint is a classic algorithmic problem with multiple applications in data mining and machine learning. We study this classic problem in the fully dynamic setting, where elements…
Submodular maximization is a general optimization problem with a wide range of applications in machine learning (e.g., active learning, clustering, and feature selection). In large-scale optimization, the parallel running time of an…
The standard oracle model for matroid algorithms assumes that each independence query can be answered in constant time, regardless of the size of the queried set. While this abstraction has underpinned much of the theoretical progress in…
We present a practical and powerful new framework for both unconstrained and constrained submodular function optimization based on discrete semidifferentials (sub- and super-differentials). The resulting algorithms, which repeatedly compute…
The classical problem of maximizing a submodular function under a matroid constraint is considered. Defining a new measure for the increments made by the greedy algorithm at each step, called the discriminant, improved approximation ratio…