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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

The problem of non-monotone $k$-submodular maximization under a knapsack constraint ($\kSMK$) over the ground set size $n$ has been raised in many applications in machine learning, such as data summarization, information propagation, etc.…

Data Structures and Algorithms · Computer Science 2023-09-22 Dung T. K. Ha , Canh V. Pham , Tan D. Tran , Huan X. Hoang

In machine learning and big data, the optimization objectives based on set-cover, entropy, diversity, influence, feature selection, etc. are commonly modeled as submodular functions. Submodular (function) maximization is generally NP-hard,…

Data Structures and Algorithms · Computer Science 2022-12-13 Haotian Zhang , Rao Li , Zewei Wu , Guodong Sun

In this work we present the first practical $\left(\frac{1}{e}-\epsilon\right)$-approximation algorithm to maximise a general non-negative submodular function subject to a matroid constraint. Our algorithm is based on combining the…

Data Structures and Algorithms · Computer Science 2017-03-22 Pau Segui-Gasco , Hyo-Sang Shin

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…

Data Structures and Algorithms · Computer Science 2018-11-20 Teng Li , Hyo-Sang Shin , Antonios Tsourdos

The classical problem of maximizing a submodular function under a matroid constraint is considered. Defining a new measure for the increments made by the greedy algorithm at each step, called the discriminant, improved approximation ratio…

Data Structures and Algorithms · Computer Science 2018-10-31 Nived Rajaraman , Rahul Vaze

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

The need for real time analysis of rapidly producing data streams (e.g., video and image streams) motivated the design of streaming algorithms that can efficiently extract and summarize useful information from massive data "on the fly".…

Data Structures and Algorithms · Computer Science 2017-12-27 Baharan Mirzasoleiman , Stefanie Jegelka , Andreas Krause

In this paper, we study the problem of maximizing $k$-submodular functions subject to a knapsack constraint. For monotone objective functions, we present a $\frac{1}{2}(1-e^{-2})\approx 0.432$ greedy approximation algorithm. For the…

Data Structures and Algorithms · Computer Science 2023-09-18 Hao Xiao , Qian Liu , Yang Zhou , Min Li

We consider the problem of maximizing a nonnegative (possibly non-monotone) submodular set function with or without constraints. Feige et al. [FOCS'07] showed a 2/5-approximation for the unconstrained problem and also proved that no…

Data Structures and Algorithms · Computer Science 2010-07-12 Shayan Oveis Gharan , Jan Vondrák

We consider fast algorithms for monotone submodular maximization with a general matroid constraint. We present a randomized $(1 - 1/e - \epsilon)$-approximation algorithm that requires $\tilde{O}_{\epsilon}(\sqrt{r} n)$ independence oracle…

Data Structures and Algorithms · Computer Science 2024-05-02 Yusuke Kobayashi , Tatsuya Terao

Submodular optimization has received significant attention in both practice and theory, as a wide array of problems in machine learning, auction theory, and combinatorial optimization have submodular structure. In practice, these problems…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-10-04 Paul Liu , Jan Vondrak

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

Optimization and Control · Mathematics 2016-10-31 Insoon Yang , Samuel A. Burden , Ram Rajagopal , S. Shankar Sastry , Claire J. Tomlin

We consider the problem of maximizing a non-monotone DR-submodular function subject to a cardinality constraint. Diminishing returns (DR) submodularity is a generalization of the diminishing returns property for functions defined over the…

Data Structures and Algorithms · Computer Science 2017-09-05 Ali Khodabakhsh , Evdokia Nikolova

We consider the problem of maximizing a monotone submodular function under a knapsack constraint. We show that, for any fixed $\epsilon > 0$, there exists a polynomial-time algorithm with an approximation ratio $1-c/e-\epsilon$, where $c…

Data Structures and Algorithms · Computer Science 2016-07-18 Yuichi Yoshida

We consider the problem of maximizing a submodular function with access to a noisy value oracle for the function instead of an exact value oracle. Similar to prior work, we assume that the noisy oracle is persistent in that multiple calls…

Data Structures and Algorithms · Computer Science 2026-01-01 Kshipra Bhawalkar , Yang Cai , Zhe Feng , Christopher Liaw , Tao Lin

This paper studies the computational complexity of a robust variant of a two-stage submodular minimization problem that we call Robust Submodular Minimizer. In this problem, we are given $k$ submodular functions~$f_1,\dots,f_k$ over a set…

Data Structures and Algorithms · Computer Science 2024-07-30 Naonori Kakimura , Ildikó Schlotter

In this paper we study the extraction of representative elements in the data stream model in the form of submodular maximization. Different from the previous work on streaming submodular maximization, we are interested only in the recent…

Data Structures and Algorithms · Computer Science 2016-11-02 Jiecao Chen , Huy L. Nguyen , Qin Zhang

We consider two classic problems: maximum coverage and monotone submodular maximization subject to a cardinality constraint. [Nemhauser--Wolsey--Fisher '78] proved that the greedy algorithm provides an approximation of $1-1/e$ for both…

Data Structures and Algorithms · Computer Science 2025-03-26 Yuval Filmus , Roy Schwartz , Alexander V. Smal

In this paper, the monotone submodular maximization problem (SM) is studied. SM is to find a subset of size $\kappa$ from a universe of size $n$ that maximizes a monotone submodular objective function $f$. We show using a novel analysis…

Data Structures and Algorithms · Computer Science 2021-07-07 Victoria G. Crawford