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We study submodular maximization problems with matroid constraints, in particular, problems where the objective can be expressed via compositions of analytic and multilinear functions. We show that for functions of this form, the so-called…

Machine Learning · Computer Science 2024-12-17 Gözde Özcan , Armin Moharrer , Stratis Ioannidis

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…

Data Structures and Algorithms · Computer Science 2026-05-11 Moran Feldman , Justin Ward

We study parallel algorithms for the problem of maximizing a non-negative submodular function. Our main result is an algorithm that achieves a nearly-optimal $1/2 -\epsilon$ approximation using $O(\log(1/\epsilon) / \epsilon)$ parallel…

Data Structures and Algorithms · Computer Science 2018-12-05 Alina Ene , Huy L. Nguyen , Adrian Vladu

While greedy algorithms have long been observed to perform well on a wide variety of problems, up to now approximation ratios have only been known for their application to problems having submodular objective functions $f$. Since many…

Data Structures and Algorithms · Computer Science 2018-01-16 J. David Smith , My T. Thai

We demonstrate that from an algorithm guaranteeing an approximation factor for the ratio of submodular (RS) optimization problem, we can build another algorithm having a different kind of approximation guarantee -- weaker than the classical…

Data Structures and Algorithms · Computer Science 2022-09-12 Pierre Perrault , Jennifer Healey , Zheng Wen , Michal Valko

We introduce the problem of maximizing approximately $k$-submodular functions subject to size constraints. In this problem, one seeks to select $k$-disjoint subsets of a ground set with bounded total size or individual sizes, and maximum…

Data Structures and Algorithms · Computer Science 2021-01-19 Leqian Zheng , Hau Chan , Grigorios Loukides , Minming Li

We consider classes of objective functions of cardinality constrained maximization problems for which the greedy algorithm guarantees a constant approximation. We propose the new class of $\gamma$-$\alpha$-augmentable functions and prove…

Discrete Mathematics · Computer Science 2022-10-05 Yann Disser , David Weckbecker

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

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 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 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…

Data Structures and Algorithms · Computer Science 2016-08-15 Alina Ene , Huy L. Nguyen

An effective technique for solving optimization problems over massive data sets is to partition the data into smaller pieces, solve the problem on each piece and compute a representative solution from it, and finally obtain a solution…

Data Structures and Algorithms · Computer Science 2015-06-23 Vahab Mirrokni , Morteza Zadimoghaddam

We briefly discuss the greedy method and a couple of its more efficient variants for approximately maximizing monotone submodular functions.

Optimization and Control · Mathematics 2025-10-21 Alen Alexanderian

We consider a problem of maximizing a monotone DR-submodular function under multiple order-consistent knapsack constraints on a distributive lattice. Since a distributive lattice is used to represent a dependency constraint, the problem can…

Data Structures and Algorithms · Computer Science 2019-07-10 Takanori Maehara , So Nakashima , Yutaro Yamaguchi

Submodular continuous functions are a category of (generally) non-convex/non-concave functions with a wide spectrum of applications. We characterize these functions and demonstrate that they can be maximized efficiently with approximation…

Machine Learning · Computer Science 2019-05-07 Andrew An Bian , Baharan Mirzasoleiman , Joachim M. Buhmann , Andreas Krause

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…

Machine Learning · Computer Science 2014-12-01 Baharan Mirzasoleiman , Ashwinkumar Badanidiyuru , Amin Karbasi , Jan Vondrak , Andreas Krause

We present a simple performance bound for the greedy scheme in string optimization problems that obtains strong results. Our approach vastly generalizes the group of previously established greedy curvature bounds by Conforti and…

Systems and Control · Electrical Eng. & Systems 2026-05-11 Brandon Van Over , Bowen Li , Edwin K. P. Chong , Ali Pezeshki

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 greedy strategy is an approximation algorithm to solve optimization problems arising in decision making with multiple actions. How good is the greedy strategy compared to the optimal solution? In this survey, we mainly consider two…

Optimization and Control · Mathematics 2019-05-10 Yajing Liu , Edwin K. P. Chong , Ali Pezeshki , Zhenliang Zhang

Constrained maximization of submodular functions poses a central problem in combinatorial optimization. In many realistic scenarios, a number of agents need to maximize multiple submodular objectives over the same ground set. We study such…

Data Structures and Algorithms · Computer Science 2024-07-22 Georgios Amanatidis , Georgios Birmpas , Philip Lazos , Stefano Leonardi , Rebecca Reiffenhäuser