We study the d-dimensional knapsack problem in the data streaming model. The knapsack is modelled as a d-dimensional integer vector of capacities. For simplicity, we assume that the input is scaled such that all capacities are 1. There is an input stream of n items, each item is modelled as a d-dimensional integer column of non-negative integer weights and a scalar profit. The input instance ha...

Given a list of d-dimensional cuboid items with associated profits, the orthogonal knapsack problem asks for a packing of a selection with maximal profit into the unit cube. We restrict the items to hypercube shapes and derive a ( 5 4 + )-approximation for the twodimensional case. In a second step we generalize our result to a ( 2 +1 2d + )approximation for d-dimensional packing.

The stochastic knapsack problem is a natural generalization of classical knapsack problem. In this problem, we are given a set of items each associated with a probability distribution on sizes and a profit, and a knapsack of unit capacity. The size of an item is unknown before inserting it into the knapsack, and it is revealed as soon as the item inserted into the knapsack. The objective is to ...

Knapsack public-key encryption schemes are based on the knapsack problem, which is NP-complete. Merkle-Hellman knapsack encryption scheme was the first concrete realization of a public-key encryption scheme. As its secure basis is superincreasing knapsack problem, it has been demonstrated to be insecure. Many variations have subsequently been proposed, whose knapsack vector density are less tha...

Since no competitive online algorithms exist for general knapsack problems, we consider online variants of knapsack problems with two assumptions: (i) the weight of each item is very small compared to the knapsack capacity; (ii) the value-to-weight ratio of each item is lower and upper bounded by two positive constants L and U . We design a deterministic threshold-based algorithm for the online...

We present algorithms for the following three-dimensional (3D) guillotine cutting problems: Unbounded Knapsack, Cutting Stock and Strip Packing. We consider the case where the items have fixed orientation and the case where orthogonal rotations around all axes are allowed. For the Unbounded 3D Knapsack problem, we extend the recurrence formula proposed by Beasley for the Rectangular Knapsack Pr...