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A $k$-submodular function naturally generalizes submodular functions by taking as input $k$ disjoint subsets, rather than a single subset. Unlike standard submodular maximization, which only requires selecting elements for the solution,…

Data Structures and Algorithms · Computer Science 2025-07-18 Chenhao Wang

We study the problem of maximizing a monotone submodular function subject to a matroid constraint, and present for it a deterministic non-oblivious local search algorithm that has an approximation guarantee of $1 - 1/e - \varepsilon$ (for…

Data Structures and Algorithms · Computer Science 2025-09-18 Niv Buchbinder , Moran Feldman

A $k$-submodular function is a generalization of the submodular set function. Many practical applications can be modeled as maximizing a $k$-submodular function, such as multi-cooperative games, sensor placement with $k$ type sensors,…

Combinatorics · Mathematics 2023-12-13 Hongyang Zhang , Wenchang Luo

The greedy algorithm for monotone submodular function maximization subject to cardinality constraint is guaranteed to approximate the optimal solution to within a $1-1/e$ factor. Although it is well known that this guarantee is essentially…

Data Structures and Algorithms · Computer Science 2022-02-15 Aviad Rubinstein , Junyao Zhao

A deterministic approximation algorithm is presented for the maximization of non-monotone submodular functions over a ground set of size $n$ subject to cardinality constraint $k$; the algorithm is based upon the idea of interlacing two…

Data Structures and Algorithms · Computer Science 2019-10-28 Alan Kuhnle

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 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

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 analyze the performance of the greedy algorithm, and also a discrete semi-gradient based algorithm, for maximizing the sum of a suBmodular and suPermodular (BP) function (both of which are non-negative monotone non-decreasing) under two…

Discrete Mathematics · Computer Science 2018-01-24 Wenruo Bai , Jeffrey A. Bilmes

In this paper, we apply a Threshold-Decreasing Algorithm to maximize $k$-submodular functions under a matroid constraint, which reduces the query complexity of the algorithm compared to the greedy algorithm with little loss in approximation…

Data Structures and Algorithms · Computer Science 2023-07-27 Shuxian Niu , Qian Liu , Yang Zhou , Min Li

The standard greedy algorithm has been recently shown to enjoy approximation guarantees for constrained non-submodular nondecreasing set function maximization. While these recent results allow to better characterize the empirical success of…

Social and Information Networks · Computer Science 2019-10-09 Khashayar Gatmiry , Manuel Gomez-Rodriguez

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 investigate the performance of a deterministic GREEDY algorithm for the problem of maximizing functions under a partition matroid constraint. We consider non-monotone submodular functions and monotone subadditive functions. Even though…

Discrete Mathematics · Computer Science 2019-02-22 Tobias Friedrich , Andreas Göbel , Frank Neumann , Francesco Quinzan , Ralf Rothenberger

Monotone submodular maximization with a knapsack constraint is NP-hard. Various approximation algorithms have been devised to address this optimization problem. In this paper, we revisit the widely known modified greedy algorithm. First, we…

Data Structures and Algorithms · Computer Science 2021-01-14 Jing Tang , Xueyan Tang , Andrew Lim , Kai Han , Chongshou Li , Junsong Yuan

Submodular maximization has been widely studied over the past decades, mostly because of its numerous applications in real-world problems. It is well known that the standard greedy algorithm guarantees a worst-case approximation factor of…

Data Structures and Algorithms · Computer Science 2020-02-12 Alfredo Torrico , Mohit Singh , Sebastian Pokutta

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

In the classical selection problem, the input consists of a collection of elements and the goal is to pick a subset of elements from the collection such that some objective function $f$ is maximized. This problem has been studied…

Data Structures and Algorithms · Computer Science 2021-09-06 Sofia Maria Nikolakaki , Alina Ene , Evimaria Terzi

In this paper, we study the tradeoff between the approximation guarantee and adaptivity for the problem of maximizing a monotone submodular function subject to a cardinality constraint. The adaptivity of an algorithm is the number of…

Data Structures and Algorithms · Computer Science 2018-11-01 Alina Ene , Huy L. Nguyen

The maximization of submodular functions have found widespread application in areas such as machine learning, combinatorial optimization, and economics, where practitioners often wish to enforce various constraints; the matroid constraint…

Data Structures and Algorithms · Computer Science 2023-05-02 Monika Henzinger , Paul Liu , Jan Vondrak , Da Wei Zheng

We consider a class of discrete optimization problems that aim to maximize a submodular objective function subject to a distributed partition matroid constraint. More precisely, we consider a networked scenario in which multiple agents…

Optimization and Control · Mathematics 2020-11-19 Alexander Robey , Arman Adibi , Brent Schlotfeldt , George J. Pappas , Hamed Hassani