Efficient Algorithms for the Knapsack Sharing Problem.

In this paper, we propose two efficient algorithms in order to approximately solve the Knapsack Sharing Problem (KSP). In KSP, we have a knapsack of capicity c and a set of n objects, where each object j, j=1,...,n, is associated with a profit pj and a weight wj. The set of objects is divided into m different classes of objects and, the aim is to determine a subset of objects to be included in the knapsack which realizes a max-min value over all classes.