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Consider costly and time-consuming tasks that add up to the success of a project, and must be fitted into a given time-frame. This is an instance of the classic budgeted maximization (knapsack) problem, which admits an FPTAS. Now assume an…

Computer Science and Game Theory · Computer Science 2026-04-10 Ilan Doron-Arad , Hadas Shachnai , Gilad Shmerler , Inbal Talgam-Cohen

Following the work of Anily et al., we consider a variant of bin packing, called "bin packing with general cost structures" (GCBP) and design an asymptotic fully polynomial time approximation scheme (AFPTAS) for this problem. In the classic…

Data Structures and Algorithms · Computer Science 2009-06-30 Leah Epstein , Asaf Levin

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

The 0-1 knapsack problem is a well-known combinatorial optimisation problem. Approximation algorithms have been designed for solving it and they return provably good solutions within polynomial time. On the other hand, genetic algorithms…

Neural and Evolutionary Computing · Computer Science 2014-04-04 Jun He , Feidun He , Hongbin Dong

We introduce and study a novel generalization of the classical Knapsack Problem (KP), called the Colored Knapsack Problem (CKP). In this problem, the items are partitioned into classes of colors and the packed items need to be ordered such…

Optimization and Control · Mathematics 2026-02-13 Fabio Ciccarelli , Alexander Helber , Erik Mühmer

An unconstrained nonlinear binary optimization problem of selecting a maximum expected value subset of items is considered. Each item is associated with a profit and probability. Each of the items succeeds or fails independently with the…

Computational Complexity · Computer Science 2017-06-23 Noam Goldberg , Gabor Rudolf

The Replenishment Storage problem (RSP) is to minimize the storage capacity requirement for a deterministic demand, multi-item inventory system where each item has a given reorder size and cycle length. The reorders can only take place at…

Data Structures and Algorithms · Computer Science 2020-10-06 Dorit S. Hochbaum , Xu Rao

We study the $K$-item knapsack problem (i.e., $1.5$-dimensional KP), which is a generalization of the famous 0-1 knapsack problem (i.e., $1$-dimensional KP) in which an upper bound $K$ is imposed on the number of items selected. This…

Data Structures and Algorithms · Computer Science 2020-12-15 Wenxin Li , Joohyun Lee

This paper introduces the Simultaneous assignment problem. Let us given a graph with a weight and a capacity function on its edges, and a set of its subgraphs along with a degree upper bound function for each of them. We are also given a…

Data Structures and Algorithms · Computer Science 2023-01-24 Péter Madarasi

In this paper, we investigate the computational complexity of the knapsack problem and subset sum problem for the following tropical algebraic structures. We consider the semigroup of square matrices of size $k \times k$ with non-negative…

Combinatorics · Mathematics 2026-05-11 I. M. Buchinskiy , M. V. Kotov , A. V. Treier

Since its inception in the mid-60s, the inventory staggering problem has been explored and exploited in a wide range of application domains, such as production planning, stock control systems, warehousing, and aerospace/defense logistics.…

Data Structures and Algorithms · Computer Science 2025-06-13 Noga Alon , Danny Segev

The main contribution of this paper resides in developing a new algorithmic approach for addressing the continuous-time joint replenishment problem, termed $\Psi$-pairwise alignment. The latter mechanism, through which we synchronize…

Data Structures and Algorithms · Computer Science 2023-02-21 Danny Segev

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

In this work, we study the classic submodular maximization problem under knapsack constraints and beyond. We first present an $(7/16-\varepsilon)$-approximate algorithm for single knapsack constraint, which requires…

Data Structures and Algorithms · Computer Science 2020-12-22 Wenxin Li

Real-world combinatorial optimization problems are often stochastic and dynamic. Therefore, it is essential to make optimal and reliable decisions with a holistic approach. In this paper, we consider the dynamic chance-constrained knapsack…

Neural and Evolutionary Computing · Computer Science 2020-02-18 Hirad Assimi , Oscar Harper , Yue Xie , Aneta Neumann , Frank Neumann

We pursue a study of the Generalized Demand Matching problem, a common generalization of the $b$-Matching and Knapsack problems. Here, we are given a graph with vertex capacities, edge profits, and asymmetric demands on the edges. The goal…

Data Structures and Algorithms · Computer Science 2017-05-31 Sara Ahmadian , Zachary Friggstad

We present a new generalization of the bin covering problem that is known to be a strongly NP-hard problem. In our generalization there is a positive constant $\Delta$, and we are given a set of items each of which has a positive size. We…

Data Structures and Algorithms · Computer Science 2022-02-23 Asaf Levin

The world is dynamic and changes over time, thus any optimization problem used to model real life problems must address this dynamic nature, taking into account the cost of changes to a solution over time. The multistage model was…

Data Structures and Algorithms · Computer Science 2021-08-03 Yaron Fairstein , Ariel Kulik , Joseph , Naor , Danny Raz

Submodular maximization generalizes many fundamental problems in discrete optimization, including Max-Cut in directed/undirected graphs, maximum coverage, maximum facility location and marketing over social networks. In this paper we…

Data Structures and Algorithms · Computer Science 2011-01-18 Ariel Kulik , Hadas Shachnai , Tami Tamir

This paper introduces a family of learning-augmented algorithms for online knapsack problems that achieve near Pareto-optimal consistency-robustness trade-offs through a simple combination of trusted learning-augmented and worst-case…

Machine Learning · Computer Science 2025-07-10 Mohammadreza Daneshvaramoli , Helia Karisani , Adam Lechowicz , Bo Sun , Cameron Musco , Mohammad Hajiesmaili