The most efficient algorithms for solving the single-criterion {0,1}-knapsack problem are based on the concept of core, i.e., a small number of relevant variables. But this concept goes unnoticed when more than one criterion is taken into account. The main purpose of the paper is to check whether or not such a set of variables is present in bi-criteria {0-1}knapsack instances. Extensive numeric...

We consider maximizing a monotone submodular function under cardinality constraint or knapsack in the streaming setting. In particular, elements arrive sequentially and at any point of time, algorithm has access to only small fraction data stored primary memory. propose following algorithms taking O(ε− 1) passes: (1) (1 − e− 1 ε)-approximation for cardinality-constrained problem, (2) (0.5 knaps...

In this paper we consider the Knapsack Problem under Uncertainty (KPu). Given a container, the knapsack, characterized by a maximum weight that can be accommodated into and a set of items with given weight and random profit, KPu aims to define the subset of items that can be accommodated into the knapsack such that the sum of the weights of the loaded items does not exceed the knapsack maximum ...

We study a constrained version of the knapsack problem in which dependencies between items are given by the adjacencies of a graph. In the 1-neighbour knapsack problem, an item can be selected only if at least one of its neighbours is also selected. We give approximation algorithms and hardness results when the nodes have both uniform and arbitrary weight and profit functions, and when the depe...

We consider an uncertain variant of the knapsack problem that arises when the exact weight of each item is not exactly known in advance but belongs to a given interval, and the number of items whose weight differs from the nominal value is bounded by a constant. We analyze the worsening of the optimal solution value with respect to the classical problem, and exactly determine its worst-case per...

This paper considers a distributionally robust version of a quadratic knapsack problem. In this model, a subsets of items is selected to maximizes the total profit while requiring that a set of knapsack constraints be satisfied with high probability. In contrast to the stochastic programming version of this problem, we assume that only part of information on random data is known, i.e., the firs...

This paper treats the multiple-choice (continuous) knapsack problem P: n mi n mi maximize L .L cijxijsubjectto(l) I I aij x ij";b,(2)0,,;xij";1,i=I,2, i=l J=l i=l J=1 ... , n, j = 1,2, .... mi and (3) at most one of x il, x i2' ... , x im. is positive for i = 1,2, ., ., n, , where n, mi are positive integers and aij' Cij' bare nonnegative real numbers. Two approximate algorithms and an exact br...

The recent progress in solving the unbounded knapsack problem (UKP) is tightly related to the phenomenon of dominance which contributes to eliminate the non-prootable object types and reduce drastically the solutions search space. We focus here on the analysis of the computational results obtained by us by (EDUK) for EEcient Dynamic programming for UKP. This new dynamic programming algorithm is...

This paper is dedicated to a study of different extensions of the classical knapsack problem to the case when different elements of the problem formulation are subject to a degree of uncertainty described by random variables. This brings the knapsack problem into the realm of stochastic programming. Two different model formulations are proposed, based on the introduction of probability constrai...

We consider the 0–1 Incremental Knapsack Problem (IKP) where the capacity grows over time periods and if an item is placed in the knapsack in a certain period, it cannot be removed afterwards. The contribution of a packed item in each time period depends on its profit as well as on a time factor which reflects the importance of the period in the objective function. The problem calls for maximiz...