Key points are not available for this paper at this time.
A given subset A of natural numbers is said to be complete if every element of is the sum of distinct terms taken from A. This topic is strongly connected to the knapsack problem which is known to be NP complete. The main goal of the paper is to study the structure of subset sums in a higher dimension. We show 'dense' sets and generalized arithmetic progrssions in subset sums of certain sets.
Hegyvári et al. (Fri,) studied this question.