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<*application, mathematics*> Given a set of items, each with a
cost and a value, determine the number of each item to include
in a collection so that the total cost is less than some given
cost and the total value is as large as possible.

The 0/1 knapsack problem restricts the number of each items to zero or one.

Such constraint satisfaction problems are often solved using dynamic programming.

The general knapsack problem is NP-hard, and this has led to attempts to use it as the basis for public-key encryption systems. Several such attempts failed because the knapsack problems they produced were in fact solvable by polynomial-time algorithms.

[Are there any trusted knapsack-based public-key cryptosystems?].

(1995-04-10)

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