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We study the online submodular maximization problem with free disposal under a matroid constraint. Elements from some ground set arrive one by one in rounds, and the algorithm maintains a feasible set that is independent in the underlying…

Discrete Mathematics · Computer Science 2016-10-26 T-H. Hubert Chan , Zhiyi Huang , Shaofeng H. -C. Jiang , Ning Kang , Zhihao Gavin Tang

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

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

Submodular function maximization is a central problem in combinatorial optimization, generalizing many important problems including Max Cut in directed/undirected graphs and in hypergraphs, certain constraint satisfaction problems, maximum…

Computational Complexity · Computer Science 2009-02-03 Jon Lee , Vahab Mirrokni , Viswanath Nagarjan , Maxim Sviridenko

Recent progress on robust clustering led to constant-factor approximations for Robust Matroid Center. After a first combinatorial $7$-approximation that is based on a matroid intersection approach, two tight LP-based $3$-approximations were…

Data Structures and Algorithms · Computer Science 2022-11-08 Georg Anegg , Laura Vargas Koch , Rico Zenklusen

We consider the problem of maximizing submodular functions in single-pass streaming and secretaries-with-shortlists models, both with random arrival order. For cardinality constrained monotone functions, Agrawal, Shadravan, and Stein gave a…

Data Structures and Algorithms · Computer Science 2021-11-16 Paul Liu , Aviad Rubinstein , Jan Vondrak , Junyao Zhao

We study the problem of maximizing a continuous DR-submodular function that is not necessarily smooth. We prove that the continuous greedy algorithm achieves an $[(1-1/e)\OPT-\epsilon]$ guarantee when the function is monotone and…

Optimization and Control · Mathematics 2023-09-29 Duksang Lee , Nam Ho-Nguyen , Dabeen Lee

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…

Data Structures and Algorithms · Computer Science 2018-05-25 Rad Niazadeh , Tim Roughgarden , Joshua R. Wang

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 consider the maximization problem in the value oracle model of functions defined on $k$-tuples of sets that are submodular in every orthant and $r$-wise monotone, where $k\geq 2$ and $1\leq r\leq k$. We give an analysis of a…

Data Structures and Algorithms · Computer Science 2016-08-05 Justin Ward , Stanislav Zivny

In this paper, we propose the first continuous optimization algorithms that achieve a constant factor approximation guarantee for the problem of monotone continuous submodular maximization subject to a linear constraint. We first prove that…

Data Structures and Algorithms · Computer Science 2020-06-23 Moran Feldman , Amin Karbasi

We study the problem of maximizing a monotone submodular set function subject to linear packing constraints. An instance of this problem consists of a matrix $A \in [0,1]^{m \times n}$, a vector $b \in [1,\infty)^m$, and a monotone…

Data Structures and Algorithms · Computer Science 2012-05-01 Yossi Azar , Iftah Gamzu

The batched greedy strategy is an approximation algorithm to maximize a set function subject to a matroid constraint. Starting with the empty set, the batched greedy strategy iteratively adds to the current solution set a batch of elements…

Optimization and Control · Mathematics 2017-10-05 Yajing Liu , Zhenliang Zhang , Edwin K. P. Chong , Ali Pezeshki

The submodular maximization problem is widely applicable in many engineering problems where objectives exhibit diminishing returns. While this problem is known to be NP-hard for certain subclasses of objective functions, there is a greedy…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-07-01 Haoyuan Sun , David Grimsman , Jason R Marden

Consider the problem of choosing a set of actions to optimize an objective function that is a real-valued polymatroid function subject to matroid constraints. The greedy strategy provides an approximate solution to the optimization problem,…

Optimization and Control · Mathematics 2018-05-24 Yajing Liu , Edwin K. P. Chong , Ali Pezeshki

We consider the optimal coverage problem where a multi-agent network is deployed in an environment with obstacles to maximize a joint event detection probability. The objective function of this problem is non-convex and no global optimum is…

Optimization and Control · Mathematics 2017-08-15 Xinmiao Sun , Christos G. Cassandras , Xiangyu Meng

We study random order semi-streaming algorithms for submodular maximization under a wide range of combinatorial constraint classes, including matroids, matroid $p$-parity, $p$-exchange systems and $p$-systems. For most of these classes of…

Data Structures and Algorithms · Computer Science 2026-05-15 Niv Buchbinder , Moran Feldman , Siyue Liu , Sherry Sarkar

In this work, we study the problem of monotone non-submodular maximization with partition matroid constraint. Although a generalization of this problem has been studied in literature, our work focuses on leveraging properties of partition…

Data Structures and Algorithms · Computer Science 2022-05-02 Lan N. Nguyen , My T. Thai

Weak submodularity is a natural relaxation of the diminishing return property, which is equivalent to submodularity. Weak submodularity has been used to show that many (monotone) functions that arise in practice can be efficiently maximized…

Data Structures and Algorithms · Computer Science 2020-09-24 Richard Santiago , Yuichi Yoshida

This paper presents a polynomial-time $1/2$-approximation algorithm for maximizing nonnegative $k$-submodular functions. This improves upon the previous $\max\{1/3, 1/(1+a)\}$-approximation by Ward and \v{Z}ivn\'y~(SODA'14), where…

Data Structures and Algorithms · Computer Science 2015-02-27 Satoru Iwata , Shin-ichi Tanigawa , Yuichi Yoshida