(classic problem)
Definition: Given types of items of different values and volumes, find the most valuable set of items that fit in a knapsack of fixed volume. The number of items of each type is unbounded. This is an NP-hard combinatorial optimization problem.
Formal Definition: There is a knapsack of capacity c > 0 and N types of items. Each item of type t has value vt > 0 and weight wt > 0. Find the number nt > 0 of each type of item such that they fit, ∑t=1N ntwt ≤ c, and the total value, ∑t=1N ntvt, is maximized.
Also known as UKP.
See also knapsack problem, fractional knapsack problem.
Author: PEB
demonstration solutions using dynamic programming. formal definition and links to papers. Links to many papers.
If you have suggestions, corrections, or comments, please get in touch with Paul E. Black.
Entry modified 17 December 2004.
HTML page formatted Mon Sep 11 09:46:09 2006.
Cite this as:
Paul E. Black, "unbounded knapsack problem", in
Dictionary of Algorithms and Data
Structures [online], Paul E. Black, ed.,
U.S. National Institute of
Standards and Technology. 17 December 2004. (accessed TODAY)
Available from: http://www.nist.gov/dads/HTML/unboundedKnapsack.html