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Submodular optimization generalizes many classic problems in combinatorial optimization and has recently found a wide range of applications in machine learning (e.g., feature engineering and active learning). For many large-scale…

Data Structures and Algorithms · Computer Science 2023-04-11 Matthew Fahrbach , Vahab Mirrokni , Morteza Zadimoghaddam

We show that any submodular minimization (SM) problem defined on a linear constraint set with constraints having up to two variables per inequality, are 2-approximable in polynomial time. If the constraints are monotone (the two variables…

Discrete Mathematics · Computer Science 2017-05-01 Dorit S. Hochbaum

Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…

Machine Learning · Computer Science 2015-02-10 Alina Ene , Huy L. Nguyen

Submodular functions have found a wealth of new applications in data science and machine learning models in recent years. This has been coupled with many algorithmic advances in the area of submodular optimization: (SO) $\min/\max~f(S): S…

Data Structures and Algorithms · Computer Science 2019-08-23 Richard Santiago , F. Bruce Shepherd

A natural and important generalization of submodularity -- $k$-submodularity -- applies to set functions with $k$ arguments and appears in a broad range of applications, such as infrastructure design, machine learning, and healthcare. In…

Optimization and Control · Mathematics 2021-06-29 Qimeng Yu , Simge Küçükyavuz

We introduce several generalizations of classical computer science problems obtained by replacing simpler objective functions with general submodular functions. The new problems include submodular load balancing, which generalizes load…

Data Structures and Algorithms · Computer Science 2010-06-02 Zoya Svitkina , Lisa Fleischer

In many submodular optimization applications, datasets are naturally partitioned into disjoint subsets. These scenarios give rise to submodular optimization problems with partition-based constraints, where the desired solution set should be…

Data Structures and Algorithms · Computer Science 2026-01-21 Wenjing Chen , Yixin Chen , Victoria G. Crawford

Recently, it has become evident that submodularity naturally captures widely occurring concepts in machine learning, signal processing and computer vision. Consequently, there is need for efficient optimization procedures for submodular…

Machine Learning · Computer Science 2013-11-19 Stefanie Jegelka , Francis Bach , Suvrit Sra

This paper considers the minimization problem of relaxed submodular functions. For a positive integer $k$, a set function is called $k$-distant submodular if the submodular inequality holds for every pair whose symmetric difference is at…

Combinatorics · Mathematics 2025-02-06 Ryuhei Mizutani

We investigate the continuous non-monotone DR-submodular maximization problem subject to a down-closed convex solvable constraint. Our first contribution is to construct an example to demonstrate that (first-order) stationary points can…

Data Structures and Algorithms · Computer Science 2024-03-27 Shengminjie Chen , Donglei Du , Wenguo Yang , Dachuan Xu , Suixiang Gao

We develop a framework for the distributed minimization of submodular functions. Submodular functions are a discrete analog of convex functions and are extensively used in large-scale combinatorial optimization problems. While there has…

Optimization and Control · Mathematics 2018-01-23 Hassan Jaleel , Jeff Shamma

We introduce the \emph{submodular objectives chasing problem}, which generalizes many natural and previously-studied problems: a sequence of constrained submodular maximization problems is revealed over time, with both the objective and…

Data Structures and Algorithms · Computer Science 2025-11-18 Niv Buchbinder , Joseph , Naor , David Wajc

We propose an algorithm for generating explicit solutions of multiparametric mixed-integer convex programs to within a given suboptimality tolerance. The algorithm is applicable to a very general class of optimization problems, but is most…

Optimization and Control · Mathematics 2019-06-12 Danylo Malyuta , Behcet Acikmese

In this paper, we investigate a class of submodular problems which in general are very hard. These include minimizing a submodular cost function under combinatorial constraints, which include cuts, matchings, paths, etc., optimizing a…

Machine Learning · Computer Science 2019-02-28 Rishabh Iyer , Jeff Bilmes

Submodular functions are relevant to machine learning for at least two reasons: (1) some problems may be expressed directly as the optimization of submodular functions and (2) the lovasz extension of submodular functions provides a useful…

Machine Learning · Computer Science 2013-10-09 Francis Bach

In this paper, we consider the optimization problem Submodular Cover (SCP), which is to find a minimum cardinality subset of a finite universe $U$ such that the value of a submodular function $f$ is above an input threshold $\tau$. In…

Data Structures and Algorithms · Computer Science 2023-09-27 Wenjing Chen , Victoria G. Crawford

The minimum linear ordering problem (MLOP) generalizes well-known combinatorial optimization problems such as minimum linear arrangement and minimum sum set cover. MLOP seeks to minimize an aggregated cost $f(\cdot)$ due to an ordering…

Data Structures and Algorithms · Computer Science 2023-10-30 Majid Farhadi , Swati Gupta , Shengding Sun , Prasad Tetali , Michael C. Wigal

A real-valued set function is (additively) approximately submodular if it satisfies the submodularity conditions with an additive error. Approximate submodularity arises in many settings, especially in machine learning, where the function…

Data Structures and Algorithms · Computer Science 2020-10-08 Flavio Chierichetti , Anirban Dasgupta , Ravi Kumar

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…

Data Structures and Algorithms · Computer Science 2025-01-03 Solmaz S. Kia

In this paper, we investigate a class of nonconvex and nonsmooth fractional programming problems, where the numerator composed of two parts: a convex, nonsmooth function and a differentiable, nonconvex function, and the denominator consists…

Optimization and Control · Mathematics 2025-03-18 Deren Han , Min Tao , Zihao Xia