The knapsack problem with special neighbor constraints

Abstract The knapsack problem is one of the simplest and most fundamental NP-hard problems in combinatorial optimization. We consider two which contain additional constraints form directed graphs whose vertex set corresponds to item set. In one-neighbor problem, an can be chosen only if at least its neighbors chosen. all-neighbors all are For both problems, we uniform general profits weights. prove upper bounds for time complexity these when restricting graph special sets digraphs. discuss co-graphs, minimal series-parallel digraphs, trees.