In the knapsack problem, you are given a knapsack of size B ∈ Z and a set S = {a1, . . . , an} of objects with corresponding sizes and profits s(ai) ∈ Z and p(ai) ∈ Z. The goal is to find the optimal subset of objects whose total size is bounded by B and has the maximum possible total profit. This problem is also sometimes called the 0/1 knapsack problem because each object must be either in th...

This paper introduces a problem called the temporal knapsack problem, presents several algorithms for solving it, and compares their performance. The temporal knapsack problem is a generalisation of the knapsack problem and specialisation of the multidimensional (or multiconstraint) knapsack problem. It arises naturally in applications such as allocating communication bandwidth or CPUs in a mul...

The online knapsack problem is a classic resource allocation in networking and operations research. Its basic version studies how to pack arriving items of different sizes values into capacity-limited knapsack. In this paper, we study general that includes item departures, while also considering multiple knapsacks multi-dimensional sizes. We design threshold-based algorithm prove the can achiev...

The nonlinear Knapsack problem is to maximize a separable concave objective function, subject to a single "packing" constraint, in nonnegative variables. We consider this problem in integer and continuous variables, and also when the packing constraint is convex. Although the nonlinear Knapsack problem appears difficult in comparison with the linear Knapsack problem, we prove that its complexit...

Knapsack constraints are a key modeling structure in discrete optimization and form the core of many real-life problem formulations. Only recently, a cost-based filtering algorithm for Knapsack constraints was published that is based on some previously developed approximation algorithms for the Knapsack problem. In this paper, we provide an empirical evaluation of approximated consistency for K...