Related papers: Stochastic Submodular Maximization via Polynomial …
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…
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,…
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…
We study the problem of maximizing constrained non-monotone submodular functions and provide approximation algorithms that improve existing algorithms in terms of either the approximation factor or simplicity. Our algorithms combine…
The standard greedy algorithm has been recently shown to enjoy approximation guarantees for constrained non-submodular nondecreasing set function maximization. While these recent results allow to better characterize the empirical success of…
As the scales of data sets expand rapidly in some application scenarios, increasing efforts have been made to develop fast submodular maximization algorithms. This paper presents a currently the most efficient algorithm for maximizing…
We study the problem of maximizing a non-negative monotone submodular objective $f$ subject to the intersection of $k$ arbitrary matroid constraints. The natural greedy algorithm guarantees $(k+1)$-approximation for this problem, and the…
Is it possible to maximize a monotone submodular function faster than the widely used lazy greedy algorithm (also known as accelerated greedy), both in theory and practice? In this paper, we develop the first linear-time algorithm for…
We consider the maximization of a submodular objective function $f:2^U\to\mathbb{R}_{\geq 0}$, where the objective $f$ is not accessed as a value oracle but instead subject to noisy queries. We introduce a versatile adaptive sampling…
A $k$-submodular function naturally generalizes submodular functions by taking as input $k$ disjoint subsets, rather than a single subset. Unlike standard submodular maximization, which only requires selecting elements for the solution,…
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 propose subsampling as a unified algorithmic technique for submodular maximization in centralized and online settings. The idea is simple: independently sample elements from the ground set, and use simple combinatorial techniques (such…
We present a simple combinatorial $\frac{1 -e^{-2}}{2}$-approximation algorithm for maximizing a monotone submodular function subject to a knapsack and a matroid constraint. This classic problem is known to be hard to approximate within…
We consider stochastic influence maximization problems arising in social networks. In contrast to existing studies that involve greedy approximation algorithms with a 63% performance guarantee, our work focuses on solving the problem…
This article provides a comprehensive exploration of submodular maximization problems, focusing on those subject to uniform and partition matroids. Crucial for a wide array of applications in fields ranging from computer science to systems…
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.…
We study the problem of maximizing a stochastic monotone submodular function with respect to a matroid constraint. Due to the presence of diminishing marginal values in real-world problems, our model can capture the effect of stochasticity…
In this work, we present a new algorithm for maximizing a non-monotone submodular function subject to a general constraint. Our algorithm finds an approximate fractional solution for maximizing the multilinear extension of the function over…
For many optimization problems in machine learning, finding an optimal solution is computationally intractable and we seek algorithms that perform well in practice. Since computational intractability often results from pathological…
We provide theoretical bounds on the worst case performance of the greedy algorithm in seeking to maximize a normalized, monotone, but not necessarily submodular objective function under a simple partition matroid constraint. We also…