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The goal of a sequential decision making problem is to design an interactive policy that adaptively selects a group of items, each selection is based on the feedback from the past, in order to maximize the expected utility of selected…
We design new approximation algorithms for the problems of optimizing submodular and supermodular functions subject to a single matroid constraint. Specifically, we consider the case in which we wish to maximize a nondecreasing submodular…
The problem of maximizing non-negative monotone submodular functions under a certain constraint has been intensively studied in the last decade. In this paper, we address the problem for functions defined over the integer lattice. Suppose…
Submodular functions have found a wealth of new applications in data science and machine learning models in recent years. This has been coupled with many algorithmic advances in the area of submodular optimization: (SO) $\min/\max~f(S): S…
Submodular function minimization (SFM) is a fundamental discrete optimization problem which generalizes many well known problems, has applications in various fields, and can be solved in polynomial time. Owing to applications in computer…
Submodular function minimization (SFM) and matroid intersection are fundamental discrete optimization problems with applications in many fields. It is well known that both of these can be solved making $\mathrm{poly}(N)$ queries to a…
This work studies the non-monotone DR-submodular Maximization over a ground set of $n$ subject to a size constraint $k$. We propose two approximation algorithms for solving this problem named FastDrSub and FastDrSub++. FastDrSub offers an…
In this paper, we propose scalable methods for maximizing a regularized submodular function $f = g - \ell$ expressed as the difference between a monotone submodular function $g$ and a modular function $\ell$. Indeed, submodularity is…
The study of approximate matching in the Massively Parallel Computations (MPC) model has recently seen a burst of breakthroughs. Despite this progress, however, we still have a far more limited understanding of maximal matching which is one…
Classes of set functions along with a choice of ground set are a bedrock to determine and develop corresponding variants of greedy algorithms to obtain efficient solutions for combinatorial optimization problems. The class of approximate…
Optimization problems with set submodular objective functions have many real-world applications. In discrete scenarios, where the same item can be selected more than once, the domain is generalized from a 2-element set to a bounded integer…
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…
We study the problem of maximizing a monotone submodular set function subject to linear packing constraints. An instance of this problem consists of a matrix $A \in [0,1]^{m \times n}$, a vector $b \in [1,\infty)^m$, and a monotone…
The problem of maximizing nonnegative monotone submodular functions under a certain constraint has been intensively studied in the last decade, and a wide range of efficient approximation algorithms have been developed for this problem.…
It is known that greedy methods perform well for maximizing monotone submodular functions. At the same time, such methods perform poorly in the face of non-monotonicity. In this paper, we show - arguably, surprisingly - that invoking the…
In this paper, we study the non-monotone adaptive submodular maximization problem subject to a knapsack and a $k$-system constraints. The input of our problem is a set of items, where each item has a particular state drawn from a known…
Submodular function minimization (SFM) is a fundamental and efficiently solvable problem class in combinatorial optimization with a multitude of applications in various fields. Surprisingly, there is only very little known about constraint…
We study the problem of maximizing a monotone submodular function subject to a Multiple Knapsack constraint. The input is a set $I$ of items, each has a non-negative weight, and a set of bins of arbitrary capacities. Also, we are given a…
The problem of maximizing non-negative submodular functions has been studied extensively in the last few years. However, most papers consider submodular set functions. Recently, several advances have been made for the more general case of…
We consider the problem of maximizing a monotone submodular function subject to a knapsack constraint. Our main contribution is an algorithm that achieves a nearly-optimal, $1 - 1/e - \epsilon$ approximation, using…