Computing Partitions with Applications to the Knapsack Problem

@article{Horowitz1974ComputingPW,
title={Computing Partitions with Applications to the Knapsack Problem},
author={E. Horowitz and S. Sahni},
journal={J. ACM},
year={1974},
volume={21},
pages={277-292}
}

Given <italic>r</italic> numbers <italic>s</italic><subscrpt>1</subscrpt>, ···, <italic>s<subscrpt>r</subscrpt></italic>, algorithms are investigated for finding all possible combinations of these numbers which sum to <italic>M</italic>. This problem is a particular instance of the 0-1 unidimensional knapsack problem. All of the usual algorithms for this problem are investigated in terms of both asymptotic computing times and storage requirements, as well as average computing times. We develop… Expand