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This paper studies the problem of maximizing a monotone submodular function under an unknown knapsack constraint. A solution to this problem is a policy that decides which item to pack next based on the past packing history. The robustness…

Data Structures and Algorithms · Computer Science 2024-10-25 Max Klimm , Martin Knaack

This paper presents an algorithmic study of a class of covering mixed-integer linear programming problems which encompasses classic cover problems, including multidimensional knapsack, facility location and supplier selection problems. We…

Data Structures and Algorithms · Computer Science 2026-02-12 Kobe Grobben , Phablo F. S. Moura , Hande Yaman

Knapsack problems are among the most fundamental problems in optimization. In the Multiple Knapsack problem, we are given multiple knapsacks with different capacities and items with values and sizes. The task is to find a subset of items of…

Data Structures and Algorithms · Computer Science 2021-10-05 Franziska Eberle , Nicole Megow , Lukas Nölke , Bertrand Simon , Andreas Wiese

We study the correlated stochastic knapsack problem of a submodular target function, with optional additional constraints. We utilize the multilinear extension of submodular function, and bundle it with an adaptation of the relaxed linear…

Data Structures and Algorithms · Computer Science 2022-08-04 Sheng Yang , Samir Khuller , Sunav Choudhary , Subrata Mitra , Kanak Mahadik

Chance constraints are frequently used to limit the probability of constraint violations in real-world optimization problems where the constraints involve stochastic components. We study chance-constrained submodular optimization problems,…

Optimization and Control · Mathematics 2023-09-27 Xiankun Yan , Anh Viet Do , Feng Shi , Xiaoyu Qin , Frank Neumann

We consider fast algorithms for monotone submodular maximization subject to a matroid constraint. We assume that the matroid is given as input in an explicit form, and the goal is to obtain the best possible running times for important…

Data Structures and Algorithms · Computer Science 2018-11-20 Alina Ene , Huy L. Nguyen

We study the problem of maximizing a non-monotone submodular function under multiple knapsack constraints. We propose a simple discrete greedy algorithm to approach this problem, and prove that it yields strong approximation guarantees for…

Machine Learning · Computer Science 2020-02-19 Vanja Doskoč , Tobias Friedrich , Andreas Göbel , Frank Neumann , Aneta Neumann , Francesco Quinzan

We investigate a more generalized form of submodular maximization, referred to as $k$-submodular maximization, with applications across social networks and machine learning domains. In this work, we propose the multilinear extension of…

Data Structures and Algorithms · Computer Science 2023-09-13 Lingxiao Huang , Baoxiang Wang , Huanjian Zhou

We study the problem of maximizing a monotone increasing submodular function over a set of weighted elements subject to a knapsack constraint. Although this problem is NP-hard, many applications require exact solutions, as approximate…

Data Structures and Algorithms · Computer Science 2025-10-21 Sabine Münch , Stephen Raach

In the (1-dimensional) bin packing problem, we are asked to pack all the given items into bins, each of capacity one, so that the number of non-empty bins is minimized. Zhu~[Chaos, Solitons \& Fractals 2016] proposed an approximation…

Data Structures and Algorithms · Computer Science 2025-09-23 Hiroshi Fujiwara , Rina Atsumi , Hiroaki Yamamoto

We give an $\alpha(1+\epsilon)$-approximation algorithm for solving covering LPs, assuming the presence of a $(1/\alpha)$-approximation algorithm for a certain optimization problem. Our algorithm is based on a simple modification of the…

Data Structures and Algorithms · Computer Science 2020-12-18 Eklavya Sharma

We consider the problem of maximizing a non-negative submodular set function $f:2^N \rightarrow \mathbb{R}_+$ over a ground set $N$ subject to a variety of packing type constraints including (multiple) matroid constraints, knapsack…

Discrete Mathematics · Computer Science 2014-08-14 Chandra Chekuri , Jan Vondrák , Rico Zenklusen

The task of maximizing a monotone submodular function under a cardinality constraint is at the core of many machine learning and data mining applications, including data summarization, sparse regression and coverage problems. We study this…

Data Structures and Algorithms · Computer Science 2023-05-26 Silvio Lattanzi , Slobodan Mitrović , Ashkan Norouzi-Fard , Jakub Tarnawski , Morteza Zadimoghaddam

We present a simple combinatorial $\frac{1 -e^{-2}}{2}$-approximation algorithm for maximizing a monotone submodular function subject to a knapsack and a matroid constraint. This classic problem is known to be hard to approximate within…

Data Structures and Algorithms · Computer Science 2018-01-16 Kanthi K. Sarpatwar , Baruch Schieber , Hadas Shachnai

In the knapsack interdiction problem, there are $n$ items, each with a non-negative profit, interdiction cost, and packing weight. There is also an interdiction budget and a capacity. The objective is to select a set of items to interdict…

Data Structures and Algorithms · Computer Science 2026-04-24 Noah Weninger

We consider the problem of maximizing the multilinear extension of a submodular function subject a single matroid constraint or multiple packing constraints with a small number of adaptive rounds of evaluation queries. We obtain the first…

Data Structures and Algorithms · Computer Science 2018-11-12 Alina Ene , Huy L. Nguyen , Adrian Vladu

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 propose a method for finding approximate solutions to multiple-choice knapsack problems. To this aim we transform the multiple-choice knapsack problem into a bi-objective optimization problem whose solution set contains solutions of the…

Optimization and Control · Mathematics 2017-12-20 Ewa M. Bednarczuk , Janusz Miroforidis , Przemysław Pyzel

In this paper, we study the following robust optimization problem. Given an independence system and candidate objective functions, we choose an independent set, and then an adversary chooses one objective function, knowing our choice. Our…

Data Structures and Algorithms · Computer Science 2018-05-22 Yasushi Kawase , Hanna Sumita

Balkanski and Singer [5] recently initiated the study of adaptivity (or parallelism) for constrained submodular function maximization, and studied the setting of a cardinality constraint. Very recent improvements for this problem by…

Data Structures and Algorithms · Computer Science 2018-11-20 Chandra Chekuri , Kent Quanrud