Related papers: Guarantees of Stochastic Greedy Algorithms for Non…
Solving stochastic optimization problems under partial observability, where one needs to adaptively make decisions with uncertain outcomes, is a fundamental but notoriously difficult challenge. In this paper, we introduce the concept of…
The task of maximizing a monotone submodular function under a cardinality constraint is at the core of many machine learning and data mining applications, including data summarization, sparse regression and coverage problems. We study this…
We derive new results for the performance of a simple greedy algorithm for finding large independent sets and matchings in constant degree regular graphs. We show that for $r$-regular graphs with $n$ nodes and girth at least $g$, the…
Submodular functions are well-studied in combinatorial optimization, game theory and economics. The natural diminishing returns property makes them suitable for many applications. We study an extension of monotone submodular functions,…
We consider the problem of monotone, submodular maximization over a ground set of size $n$ subject to cardinality constraint $k$. For this problem, we introduce the first deterministic algorithms with linear time complexity; these…
We study the problem of scheduling sensors in a resource-constrained linear dynamical system, where the objective is to select a small subset of sensors from a large network to perform the state estimation task. We formulate this problem as…
We study adaptive combinatorial maximization, which is a core challenge in machine learning, with applications in active learning as well as many other domains. We study the Bayesian setting, and consider the objectives of maximization…
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…
Since Tinhofer proposed the MinGreedy algorithm for maximum cardinality matching in 1984, several experimental studies found the randomized algorithm to perform excellently for various classes of random graphs and benchmark instances. In…
Submodular maximization under matroid constraints is a fundamental problem in combinatorial optimization with applications in sensing, data summarization, active learning, and resource allocation. While the Sequential Greedy (SG) algorithm…
In this paper we study the adaptivity of submodular maximization. Adaptivity quantifies the number of sequential rounds that an algorithm makes when function evaluations can be executed in parallel. Adaptivity is a fundamental concept that…
We propose a theoretical framework to capture incremental solutions to cardinality constrained maximization problems. The defining characteristic of our framework is that the cardinality/support of the solution is bounded by a value…
In this paper we study the fundamental problems of maximizing a continuous non-monotone submodular function over the hypercube, both with and without coordinate-wise concavity. This family of optimization problems has several applications…
For constrained, not necessarily monotone submodular maximization, all known approximation algorithms with ratio greater than $1/e$ require continuous ideas, such as queries to the multilinear extension of a submodular function and its…
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 study a linear quadratic regulation problem with a constraint where the control input can be nonzero only at a limited number of times. Given that this constraint leads to a combinational optimization problem, we adopt a greedy method to…
Submodular optimization plays a key role in many real-world problems. In many real-world scenarios, it is also necessary to handle uncertainty, and potentially disruptive events that violate constraints in stochastic settings need to be…
We study the problem of maximizing a non-monotone submodular function subject to a cardinality constraint in the streaming model. Our main contribution is a single-pass (semi-)streaming algorithm that uses roughly $O(k / \varepsilon^2)$…
Symmetric submodular maximization is an important class of combinatorial optimization problems, including MAX-CUT on graphs and hyper-graphs. The state-of-the-art algorithm for the problem over general constraints has an approximation ratio…
An effective technique for solving optimization problems over massive data sets is to partition the data into smaller pieces, solve the problem on each piece and compute a representative solution from it, and finally obtain a solution…