An efficient pruning algorithm for value independent knapsack problem using a DAG structure

In this paper, we propose an efficient pruning algorithm to solve the value independent knapsack problem. It stores all the solutions in a directed acyclic graph (DAG) using only O(M • n) space, where n is the problem size and M is the subset summation. Our algorithm is suitable for the case of M 2n. Also, we find a symmetric property that can improve many heuristic algorithms proposed in the past.