We describe an algorithm for the 0-1 knapsack problem (KP), which relies mainly on three new ideas. The first one is to focus on what we call the core of the problem, namely, a knapsack problem ...

Since Balas and Zemel in the 1980s introduced the so-called core problem as an efficient tool for solving the Knapsack Problem, all the most successful algorithms have applied this concept. Balas and ...

This fictional dilemma, the “knapsack problem,” belongs to a class of mathematical problems famous for pushing the limits of computing. And the knapsack problem is more than a thought experiment.

The unbounded knapsack problem: given a knapsack of some capacity and a set of items that have a weight and a value, determine the maximum value of items you can place in your knapsack. The number ...