On-line algorithms for cardinality constrained bin packing problems

Abstract

The bin packing problem asks for a packing of a list of items from [0, 1] into the smallest possible number of bins having unit capacity. The κ-item bin packing problem additionally imposes the constraint that at most κ items are allowed in one bin. We present two efficient approximation algorithms for the on-line version of this problem. We show that, for increasing values of k, the asymptotic worst-case performance ratio of the first algorithm tends towards 2 and that the second algorithm has an asymptotic worst-case performance ratio of 2. Both heuristics considerably improve upon the best known result 2.7 of Krause, Shen and Schwetman. Moreover, we present algorithms for κ = 2 and κ = 3, where the result for κ = 2 is best possible. © 2001 Springer Berlin Heidelberg.