TY - GEN
T1 - Approximation schemes for packing splittable items with cardinality constraints
AU - Epstein, Leah
AU - Van Stee, Rob
PY - 2008
Y1 - 2008
N2 - We continue the study of bin packing with splittable items and cardinality constraints. In this problem, a set of items must be packed into as few bins as possible. Items may be split, but each bin may contain at most k (parts of) items, where k is some fixed constant. Complicating the problem further is the fact that items may be larger than 1, which is the size of a bin. We close this problem by providing a polynomial-time approximation scheme for it. We first present a scheme for the case k∈=∈2 and then for the general case of constant k. Additionally, we present dual approximation schemes for k∈=∈2 and constant k. Thus we show that for any ε>∈0, it is possible to pack the items into the optimal number of bins in polynomial time, if the algorithm may use bins of size 1∈+∈ε.
AB - We continue the study of bin packing with splittable items and cardinality constraints. In this problem, a set of items must be packed into as few bins as possible. Items may be split, but each bin may contain at most k (parts of) items, where k is some fixed constant. Complicating the problem further is the fact that items may be larger than 1, which is the size of a bin. We close this problem by providing a polynomial-time approximation scheme for it. We first present a scheme for the case k∈=∈2 and then for the general case of constant k. Additionally, we present dual approximation schemes for k∈=∈2 and constant k. Thus we show that for any ε>∈0, it is possible to pack the items into the optimal number of bins in polynomial time, if the algorithm may use bins of size 1∈+∈ε.
UR - http://www.scopus.com/inward/record.url?scp=49949113179&partnerID=8YFLogxK
U2 - 10.1007/978-3-540-77918-6_19
DO - 10.1007/978-3-540-77918-6_19
M3 - Conference contribution
AN - SCOPUS:49949113179
SN - 3540779175
SN - 9783540779179
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 232
EP - 245
BT - Approximation and Online Algorithms - 5th International Workshop, WAOA 2007, Revised Papers
T2 - 5th International Workshop on Approximation and Online Algorithms, WAOA 2007
Y2 - 11 October 2007 through 12 October 2007
ER -