TY - JOUR
T1 - Algorithms for the bounded set-up knapsack problem
AU - McLay, Laura A.
AU - Jacobson, Sheldon H.
N1 - Funding Information:
The authors would like to thank the Associate Editor and two anonymous referees for their insightful comments and feedback, which has resulted in a significantly improved manuscript. This research has been supported in part by the National Science Foundation (DMI-0114499) and the Air Force Office of Scientific Research (FA9550-04-1-0110).
PY - 2007/6/1
Y1 - 2007/6/1
N2 - The Bounded Set-up Knapsack Problem (BSKP) is a generalization of the Bounded Knapsack Problem (BKP), where each item type has a set-up weight and a set-up value that are included in the knapsack and the objective function value, respectively, if any copies of that item type are in the knapsack. This paper provides three dynamic programming algorithms that solve BSKP in pseudo-polynomial time and a fully polynomial-time approximation scheme (FPTAS). A key implication from these results is that the dynamic programming algorithms and the FPTAS can also be applied to BKP. One of the dynamic programming algorithms presented solves BKP with the same time and space bounds of the best known dynamic programming algorithm for BKP. Moreover, the FPTAS improves the worst-case time bound for obtaining approximate solutions to BKP as compared to using FPTASs designed for BKP or the 0-1 Knapsack Problem.
AB - The Bounded Set-up Knapsack Problem (BSKP) is a generalization of the Bounded Knapsack Problem (BKP), where each item type has a set-up weight and a set-up value that are included in the knapsack and the objective function value, respectively, if any copies of that item type are in the knapsack. This paper provides three dynamic programming algorithms that solve BSKP in pseudo-polynomial time and a fully polynomial-time approximation scheme (FPTAS). A key implication from these results is that the dynamic programming algorithms and the FPTAS can also be applied to BKP. One of the dynamic programming algorithms presented solves BKP with the same time and space bounds of the best known dynamic programming algorithm for BKP. Moreover, the FPTAS improves the worst-case time bound for obtaining approximate solutions to BKP as compared to using FPTASs designed for BKP or the 0-1 Knapsack Problem.
KW - Dynamic programming
KW - Fully polynomial-time approximation schemes
KW - Knapsack problems
UR - http://www.scopus.com/inward/record.url?scp=34047259696&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=34047259696&partnerID=8YFLogxK
U2 - 10.1016/j.disopt.2006.11.002
DO - 10.1016/j.disopt.2006.11.002
M3 - Article
AN - SCOPUS:34047259696
SN - 1572-5286
VL - 4
SP - 206
EP - 212
JO - Discrete Optimization
JF - Discrete Optimization
IS - 2
ER -