TY - JOUR
T1 - New pseudopolynomial complexity bounds for the bounded and other integer Knapsack related problems
AU - Tamir, Arie
PY - 2009/9
Y1 - 2009/9
N2 - We consider the bounded integer knapsack problem (BKP) max ∑j = 1n pj xj, subject to: ∑j = 1n wj xj ≤ C, and xj ∈ {0, 1, ..., mj}, j = 1, ..., n. We use proximity results between the integer and the continuous versions to obtain an O (n3 W2) algorithm for BKP, where W = maxj = 1, ..., n wj. The respective complexity of the unbounded case with mj = ∞, for j = 1, ..., n, is O (n2 W2). We use these results to obtain an improved strongly polynomial algorithm for the multicover problem with cyclical 1's and uniform right-hand side.
AB - We consider the bounded integer knapsack problem (BKP) max ∑j = 1n pj xj, subject to: ∑j = 1n wj xj ≤ C, and xj ∈ {0, 1, ..., mj}, j = 1, ..., n. We use proximity results between the integer and the continuous versions to obtain an O (n3 W2) algorithm for BKP, where W = maxj = 1, ..., n wj. The respective complexity of the unbounded case with mj = ∞, for j = 1, ..., n, is O (n2 W2). We use these results to obtain an improved strongly polynomial algorithm for the multicover problem with cyclical 1's and uniform right-hand side.
KW - Bounded knapsack problem
KW - Bounded multiple-choice knapsack problem
KW - Multicover problem
KW - Pseudopolynomial algorithms
UR - http://www.scopus.com/inward/record.url?scp=69549091815&partnerID=8YFLogxK
U2 - 10.1016/j.orl.2009.05.003
DO - 10.1016/j.orl.2009.05.003
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AN - SCOPUS:69549091815
SN - 0167-6377
VL - 37
SP - 303
EP - 306
JO - Operations Research Letters
JF - Operations Research Letters
IS - 5
ER -