This system is based on a type of knapsack problem.

The knapsack problem is interesting from the perspective of computer science for many reasons:

If there is a single agent, then, this problem reduces to the Knapsack problem.

The knapsack problem has been studied for more than a century, with early works dating as far back as 1897.

The following describes a dynamic programming solution for the unbounded knapsack problem.

Subset sum can also be thought of as a special case of the knapsack problem.

Combinatorial optimization problems such as parsing and the knapsack problem.

A similar dynamic programming solution for the 0/1 knapsack problem also runs in pseudo-polynomial time.

A greedy algorithm can find the optimum solution to the continuous knapsack problem.

A new quantum-inspired cuckoo search was developed to solve Knapsack problems, which shows its effectiveness.

Solving the unbounded knapsack problem can be made easier by throwing away items which will never be needed.

Mathematically the bounded knapsack problem can be formulated as:

When the costs and profits of all agents-task assignment are equal, this problem reduces to the multiple knapsack problem.

The knapsack problem has well-known methods to solve it, such as branch and bound and dynamic programming.

Finding a market-clearing allocation corresponds to solution of a simple knapsack problem, and does not require much computation.

A related problem is the partition problem, a variant of the knapsack problem from operations research.

The Merkle-Hellman system is based on the subset sum problem (a special case of the knapsack problem).

This technique was also proposed by George Dantzig as a greedy algorithm to the classic knapsack problem.

Contains the Knapsack problem.

Also in Lagrangian relaxation methods for facility location problems the problem will be reduced to instances of continuous knapsack problem.

An example of a problem that has an FPTAS is the knapsack problem.

There are many variations of the knapsack problem that have arisen from the vast number of applications of the basic problem.

The quadratic knapsack problem was discussed under that title by Gallo, Hammer, and Simeone in 1980.

The Unbounded Knapsack problem.

To use a heuristic for solving a search or a knapsack problem, it is necessary to check that the heuristic is admissible.