Related papers: Dynamic Algorithms for Matroid Submodular Maximiza…
Maximization of submodular functions under various constraints is a fundamental problem that has been studied extensively. A powerful technique that has emerged and has been shown to be extremely effective for such problems is the…
Motivated by a wide range of applications in data mining and machine learning, we consider the problem of maximizing a submodular function subject to supermodular cost constraints. In contrast to the well-understood setting of cardinality…
Submodular maximization with a cardinality constraint can model various problems, and those problems are often very large in practice. For the case where objective functions are monotone, many fast approximation algorithms have been…
Diversity maximization is a fundamental problem in web search and data mining. For a given dataset $S$ of $n$ elements, the problem requires to determine a subset of $S$ containing $k\ll n$ "representatives" which minimize some diversity…
The subspace selection problem seeks a subspace that maximizes an objective function under some constraint. This problem includes several important machine learning problems such as the principal component analysis and sparse dictionary…
Robust optimization is becoming increasingly important in machine learning applications. In this paper, we study a unified framework of robust submodular optimization. We study this problem both from a minimization and maximization…
Many important problems in discrete optimization require maximization of a monotonic submodular function subject to matroid constraints. For these problems, a simple greedy algorithm is guaranteed to obtain near-optimal solutions. In this…
In the Inverse Matroid problem, we are given a matroid, a fixed basis $B$, and an initial weight function, and the goal is to minimally modify the weights -- measured by some function -- so that $B$ becomes a maximum-weight basis. The…
We study monotone submodular maximization under general matroid constraints in the online setting. We prove that online optimization of a large class of submodular functions, namely, weighted threshold potential functions, reduces to online…
The study of combinatorial optimization problems with a submodular objective has attracted much attention in recent years. Such problems are important in both theory and practice because their objective functions are very general. Obtaining…
Submodular maximization arises in many applications, and has attracted a lot of research attentions from various areas such as artificial intelligence, finance and operations research. Previous studies mainly consider only one kind of…
In this paper, we study the problem of maximizing continuous submodular functions that naturally arise in many learning applications such as those involving utility functions in active learning and sensing, matrix approximations and network…
We investigate the performance of a deterministic GREEDY algorithm for the problem of maximizing functions under a partition matroid constraint. We consider non-monotone submodular functions and monotone subadditive functions. Even though…
In this paper, we develop the first one-pass streaming algorithm for submodular maximization that does not evaluate the entire stream even once. By carefully subsampling each element of data stream, our algorithm enjoys the tightest…
Streaming algorithms are generally judged by the quality of their solution, memory footprint, and computational complexity. In this paper, we study the problem of maximizing a monotone submodular function in the streaming setting with a…
Given a collection of monotone submodular functions, the goal of Two-Stage Submodular Maximization (2SSM) [Balkanski et al., 2016] is to restrict the ground set so an objective selected u.a.r. from the collection attains a high maximal…
We develop a dynamic version of the primal-dual method for optimization problems, and apply it to obtain the following results. (1) For the dynamic set-cover problem, we maintain an $O(f^2)$-approximately optimal solution in $O(f \cdot \log…
We study \emph{combinatorial procurement auctions}, where a buyer with a valuation function $v$ and budget $B$ wishes to buy a set of items. Each item $i$ has a cost $c_i$ and the buyer is interested in a set $S$ that maximizes $v(S)$…
In this paper, we present a thorough study of maximizing a regularized non-monotone submodular function subject to various constraints, i.e., $\max \{ g(A) - \ell(A) : A \in \mathcal{F} \}$, where $g \colon 2^\Omega \to \mathbb{R}_+$ is a…
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…