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Submodular maximization is a classic algorithmic problem with multiple applications in data mining and machine learning; there, the growing need to deal with massive instances motivates the design of algorithms balancing the quality of the…

Data Structures and Algorithms · Computer Science 2024-02-20 Georgios Amanatidis , Federico Fusco , Philip Lazos , Stefano Leonardi , Alberto Marchetti Spaccamela , Rebecca Reiffenhäuser

In this paper, we study the bandits with knapsacks (BwK) problem and develop a primal-dual based algorithm that achieves a problem-dependent logarithmic regret bound. The BwK problem extends the multi-arm bandit (MAB) problem to model the…

Machine Learning · Computer Science 2021-06-24 Xiaocheng Li , Chunlin Sun , Yinyu Ye

Obtaining strong linear relaxations of capacitated covering problems constitute a major technical challenge even for simple settings. For one of the most basic cases, the Knapsack-Cover (Min-Knapsack) problem, the relaxation based on…

Data Structures and Algorithms · Computer Science 2019-12-30 Andrés Fielbaum , Ignacio Morales , José Verschae

Recently various optimization problems, such as Mixed Integer Linear Programming Problems (MILPs), have undergone comprehensive investigation, leveraging the capabilities of machine learning. This work focuses on learning-based solutions…

Machine Learning · Computer Science 2024-06-21 Zhentao Tan , Yadong Mu

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

In the knapsack problem under explorable uncertainty, we are given a knapsack instance with uncertain item profits. Instead of having access to the precise profits, we are only given uncertainty intervals that are guaranteed to contain the…

Data Structures and Algorithms · Computer Science 2025-07-04 Jens Schlöter

The min-knapsack problem with compactness constraints extends the classical knapsack problem, in the case of ordered items, by introducing a restriction ensuring that they cannot be too far apart. This problem has applications in…

Optimization and Control · Mathematics 2025-04-28 Hubert Villuendas , Mathieu Besançon , Jérôme Malick

First, we study geometric variants of the standard set cover motivated by assignment of directional antenna and shipping with deadlines, providing the first known polynomial-time exact solutions. Next, we consider the following general…

Computational Complexity · Computer Science 2009-09-30 Piotr Berman , Marek Karpinski , Andrzej Lingas

Weighted model counting (WMC) consists of computing the weighted sum of all satisfying assignments of a propositional formula. WMC is well-known to be #P-hard for exact solving, but admits a fully polynomial randomized approximation scheme…

Artificial Intelligence · Computer Science 2020-07-14 Ralph Abboud , İsmail İlkan Ceylan , Radoslav Dimitrov

We consider the classic scheduling problem of minimizing the total weighted flow-time on a single machine (min-WPFT), when preemption is allowed. In this problem, we are given a set of $n$ jobs, each job having a release time $r_j$, a…

Data Structures and Algorithms · Computer Science 2018-07-27 Uriel Feige , Janardhan Kulkarni , Shi Li

Submodular function maximization is a central problem in combinatorial optimization, generalizing many important problems including Max Cut in directed/undirected graphs and in hypergraphs, certain constraint satisfaction problems, maximum…

Computational Complexity · Computer Science 2009-02-03 Jon Lee , Vahab Mirrokni , Viswanath Nagarjan , Maxim Sviridenko

In this paper, we study the Dynamic Parameterized Subset Sampling (DPSS) problem in the Word RAM model. In DPSS, the input is a set,~$S$, of~$n$ items, where each item,~$x$, has a non-negative integer weight,~$w(x)$. Given a pair of query…

Data Structures and Algorithms · Computer Science 2024-09-27 Junhao Gan , Seeun William Umboh , Hanzhi Wang , Anthony Wirth , Zhuo Zhang

Knapsack and Partition are two important additive problems whose fine-grained complexities in the $(1-\varepsilon)$-approximation setting are not yet settled. In this work, we make progress on both problems by giving improved algorithms. -…

Data Structures and Algorithms · Computer Science 2023-01-24 Mingyang Deng , Ce Jin , Xiao Mao

We consider the machine covering problem for selfish related machines. For a constant number of machines, m, we show a monotone polynomial time approximation scheme (PTAS) with running time that is linear in the number of jobs. It uses a…

Computer Science and Game Theory · Computer Science 2007-05-23 Leah Epstein , Rob van Stee

In this paper, we introduce online knapsack problems with a resource buffer. In the problems, we are given a knapsack with capacity $1$, a buffer with capacity $R\ge 1$, and items that arrive one by one. Each arriving item has to be taken…

Data Structures and Algorithms · Computer Science 2019-09-24 Xin Han , Yasushi Kawase , Kazuhisa Makino , Haruki Yokomaku

Binary quadratic programming problems have attracted much attention in the last few decades due to their potential applications. This type of problems are NP-hard in general, and still considered a challenge in the design of efficient…

Data Structures and Algorithms · Computer Science 2014-11-20 Khaled Elbassioni , Trung Thanh Nguyen

The knapsack problem (KP) is a very famous NP-hard problem in combinatorial optimization. Also its generalization to multiple dimensions named d-dimensional knapsack problem (d-KP) and to multiple knapsacks named multiple knapsack problem…

Computational Complexity · Computer Science 2016-11-24 Carolin Albrecht , Frank Gurski , Jochen Rethmann , Eda Yilmaz

We present approximation algorithms for maximum independent set of pseudo-disks in the plane, both in the weighted and unweighted cases. For the unweighted case, we prove that a local search algorithm yields a \PTAS. For the weighted case,…

Computational Geometry · Computer Science 2011-03-09 Timothy M. Chan , Sariel Har-Peled

This paper gives a dichotomy theorem for the complexity of computing the partition function of an instance of a weighted Boolean constraint satisfaction problem. The problem is parameterised by a finite set F of non-negative functions that…

Computational Complexity · Computer Science 2009-02-23 Martin Dyer , Leslie Ann Goldberg , Mark Jerrum

The knapsack problem is one of the classical problems in combinatorial optimization: Given a set of items, each specified by its size and profit, the goal is to find a maximum profit packing into a knapsack of bounded capacity. In the…

Data Structures and Algorithms · Computer Science 2020-12-02 Susanne Albers , Arindam Khan , Leon Ladewig