Related papers: Submodular Maximization Beyond Non-negativity: Gua…
We introduce the \emph{submodular objectives chasing problem}, which generalizes many natural and previously-studied problems: a sequence of constrained submodular maximization problems is revealed over time, with both the objective and…
Coordinating multiple agents to collaboratively maximize submodular functions in unpredictable environments is a critical task with numerous applications in machine learning, robot planning and control. The existing approaches, such as the…
We study submodular maximization problems with matroid constraints, in particular, problems where the objective can be expressed via compositions of analytic and multilinear functions. We show that for functions of this form, the so-called…
We present a branch and bound method for maximizing an arbitrary set function h mapping 2^V to R. By decomposing h as f-g, where f is a submodular function and g is the cut function of a (simple, undirected) graph G with vertex set V, our…
We investigate the existence of approximation algorithms for maximization of submodular functions, that run in fixed parameter tractable (FPT) time. Given a non-decreasing submodular set function $v: 2^X \to \mathbb{R}$ the goal is to…
In this paper, we investigate a class of submodular problems which in general are very hard. These include minimizing a submodular cost function under combinatorial constraints, which include cuts, matchings, paths, etc., optimizing a…
We consider a class of submodular maximization problems in which decision-makers have limited access to the objective function. We explore scenarios where the decision-maker can observe only pairwise information, i.e., can evaluate the…
Submodular maximization is one of the central topics in combinatorial optimization. It has found numerous applications in the real world. In the past decades, a series of algorithms have been proposed for this problem. However, most of the…
We study parallel algorithms for the problem of maximizing a non-negative submodular function. Our main result is an algorithm that achieves a nearly-optimal $1/2 -\epsilon$ approximation using $O(\log(1/\epsilon) / \epsilon)$ parallel…
Submodular functions have applications throughout machine learning, but in many settings, we do not have direct access to the underlying function $f$. We focus on stochastic functions that are given as an expectation of functions over a…
We consider the problem of maximizing a non-negative monotone submodular function subject to a knapsack constraint, which is also known as the Budgeted Submodular Maximization (BSM) problem. Sviridenko (2004) showed that by guessing 3…
We consider the problem of maximizing the sum of a monotone submodular function and a linear function subject to a general solvable polytope constraint. Recently, Sviridenko et al. (2017) described an algorithm for this problem whose…
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 $k$-submodular function is an extension of a submodular function in that its input is given by $k$ disjoint subsets instead of a single subset. For unconstrained nonnegative $k$-submodular maximization, Ward and \v{Z}ivn\'y proposed a…
In this paper, we study the problem of maximizing the difference between an adaptive submodular (revenue) function and an non-negative modular (cost) function under the adaptive setting. The input of our problem is a set of $n$ items, where…
In submodular $k$-partition, the input is a non-negative submodular function $f$ defined over a finite ground set $V$ (given by an evaluation oracle) along with a positive integer $k$ and the goal is to find a partition of the ground set…
Submodular maximization has been widely studied over the past decades, mostly because of its numerous applications in real-world problems. It is well known that the standard greedy algorithm guarantees a worst-case approximation factor of…
In this paper we consider the problem of maximizing a non-negative submodular function subject to a cardinality constraint in the data stream model. Previously, the best known algorithm for this problem was a $5.828$-approximation…
Randomization is a fundamental tool used in many theoretical and practical areas of computer science. We study here the role of randomization in the area of submodular function maximization. In this area most algorithms are randomized, and…
We extend the work of Narasimhan and Bilmes [30] for minimizing set functions representable as a difference between submodular functions. Similar to [30], our new algorithms are guaranteed to monotonically reduce the objective function at…