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Many algorithms for maximizing a monotone submodular function subject to a knapsack constraint rely on the natural greedy heuristic. We present a novel refined analysis of this greedy heuristic which enables us to: $(1)$ reduce the…

Data Structures and Algorithms · Computer Science 2021-03-16 Ariel Kulik , Roy Schwartz , Hadas Shachnai

We study dynamic algorithms for the problem of maximizing a monotone submodular function over a stream of $n$ insertions and deletions. We show that any algorithm that maintains a $(0.5+\epsilon)$-approximate solution under a cardinality…

Data Structures and Algorithms · Computer Science 2022-04-19 Xi Chen , Binghui Peng

We present an efficient algorithm to find non-empty minimizers of a symmetric submodular function over any family of sets closed under inclusion. This for example includes families defined by a cardinality constraint, a knapsack constraint,…

Data Structures and Algorithms · Computer Science 2013-10-08 Michel X. Goemans , José A. Soto

The simplex algorithm for linear programming is based on the fact that any local optimum with respect to the polyhedral neighborhood is also a global optimum. We show that a similar result carries over to submodular maximization. In…

Data Structures and Algorithms · Computer Science 2017-12-01 Simon Bruggmann , Rico Zenklusen

We investigate the performance of the standard Greedy algorithm for cardinality constrained maximization of non-submodular nondecreasing set functions. While there are strong theoretical guarantees on the performance of Greedy for…

Discrete Mathematics · Computer Science 2019-05-15 Andrew An Bian , Joachim M. Buhmann , Andreas Krause , Sebastian Tschiatschek

Let $V$ be a finite set of $n$ elements, $f: 2^V \rightarrow \mathbb{R}_+$ be a nonnegative monotone supermodular function, and $k$ be a positive integer no greater than $n$. This paper addresses the problem of maximizing $f(S)$ over all…

Optimization and Control · Mathematics 2025-10-23 Xujin Chen , Xiaodong Hu , Changjun Wang , Qingjie Ye

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…

Machine Learning · Computer Science 2021-02-25 Eric Balkanski , Sharon Qian , Yaron Singer

We consider the problem of maximizing a monotone submodular function in a $k$-exchange system. These systems, introduced by Feldman et al., generalize the matroid k-parity problem in a wide class of matroids and capture many other…

Data Structures and Algorithms · Computer Science 2012-03-13 Justin Ward

We show that the recent breakthrough result of [Buchbinder and Feldman, FOCS'24] could further lead to a deterministic $(1-\kappa_{f}/e-\varepsilon)$-approximate algorithm for maximizing a submodular function with curvature $\kappa_{f}$…

Data Structures and Algorithms · Computer Science 2024-09-06 Wenxin Li

We introduce efficient $(1+\varepsilon)$-approximation algorithms for the binary matrix factorization (BMF) problem, where the inputs are a matrix $\mathbf{A}\in\{0,1\}^{n\times d}$, a rank parameter $k>0$, as well as an accuracy parameter…

Data Structures and Algorithms · Computer Science 2023-06-06 Ameya Velingker , Maximilian Vötsch , David P. Woodruff , Samson Zhou

First, for the for the submodular $k$-secretary problem with shortlists [1], we provide a near optimal $1-1/e-\epsilon$ approximation using shortlist of size $O(k poly(1/\epsilon))$. In particular, we improve the size of shortlist used in…

Data Structures and Algorithms · Computer Science 2021-02-22 Mohammad Shadravan

In this paper, we introduce a novel technique for constrained submodular maximization, inspired by barrier functions in continuous optimization. This connection not only improves the running time for constrained submodular maximization but…

Machine Learning · Computer Science 2020-02-11 Ashwinkumar Badanidiyuru , Amin Karbasi , Ehsan Kazemi , Jan Vondrak

We give improved multi-pass streaming algorithms for the problem of maximizing a monotone or arbitrary non-negative submodular function subject to a general $p$-matchoid constraint in the model in which elements of the ground set arrive one…

Data Structures and Algorithms · Computer Science 2021-02-22 Chien-Chung Huang , Theophile Thiery , Justin Ward

Distributed maximization of a submodular function in the MapReduce (MR) model has received much attention, culminating in two frameworks that allow a centralized algorithm to be run in the MR setting without loss of approximation, as long…

Data Structures and Algorithms · Computer Science 2024-09-17 Yixin Chen , Tonmoy Dey , Alan Kuhnle

Submodular optimization has numerous applications such as crowdsourcing and viral marketing. In this paper, we study the fundamental problem of non-negative submodular function maximization subject to a $k$-system constraint, which…

Data Structures and Algorithms · Computer Science 2021-06-16 Kai Han , Shuang Cui , Tianshuai Zhu , Jing Tang , Benwei Wu , He Huang

We present a practical and powerful new framework for both unconstrained and constrained submodular function optimization based on discrete semidifferentials (sub- and super-differentials). The resulting algorithms, which repeatedly compute…

Data Structures and Algorithms · Computer Science 2013-08-13 Rishabh Iyer , Stefanie Jegelka , Jeff Bilmes

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…

Systems and Control · Electrical Eng. & Systems 2022-10-19 Benjamin Biggs , James McMahon , Philip Baldoni , Daniel J. Stilwell

In this paper, we consider the optimization problem \scpl (\scp), which is to find a minimum cost subset of a ground set $U$ such that the value of a submodular function $f$ is above a threshold $\tau$. In contrast to most existing work on…

Data Structures and Algorithms · Computer Science 2022-11-10 Victoria G. Crawford

In a stochastic probing problem we are given a universe $E$, where each element $e \in E$ is active independently with probability $p_e$, and only a probe of e can tell us whether it is active or not. On this universe we execute a process…

Data Structures and Algorithms · Computer Science 2014-02-19 Marek Adamczyk , Maxim Sviridenko , Justin Ward

In this paper we design a new primal-dual algorithm for the classic discrete optimization problem of maximizing a monotone submodular function subject to a cardinality constraint achieving the optimal approximation of $(1-1/e)$. This…

Data Structures and Algorithms · Computer Science 2023-11-15 Deeparnab Chakrabarty , Luc Cote