A parallel algorithm for the knapsack problem

Journal Article · Tue May 01 00:00:00 EDT 1984 · IEEE Trans. Comput.; (United States)

DOI:https://doi.org/10.1109/TC.1984.1676456· OSTI ID:5839381

Karnin, E D

A time-memory-processor tradeoff for the knapsack problem is proposed. While an exhaustive search over all possible solutions of an n-component knapsack required T = O(2 /SUP n/ ) running time, our parallel algorithm solves the problem in O(2 /SUP n/2/ ) operations and requires only O(2 /SUP n/6/ ) processors and memory cells. It is an improvement over previous time-memory-processor tradeoffs, being the only one which outperforms the C /SUB m/ C /SUB s/ = 2 /SUP n/ curve. C /SUB m/ is the cost of the machine, i.e., the number of its processors and memory cells, and C /SUB s/ is the cost per solution, which is the product of the machine cost by the running time.

• OSTI ID: 5839381
• Journal Information: IEEE Trans. Comput.; (United States), Vol. C-33:5
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
ALGORITHMS
COST
DIGITAL COMPUTERS
EFFICIENCY
MEMORY DEVICES
NUMERICAL SOLUTION
PARALLEL PROCESSING
COMPUTERS
MATHEMATICAL LOGIC
PROGRAMMING
990200* - Mathematics & Computers