An annotated bibliography of combinatorial optimization problems with fixed cardinality constraints
Discrete Applied Mathematics - Special issue: 2nd cologne/twente workshop on graphs and combinatorial optimization (CTW 2003)
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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 k-item bin packing problem additionally imposes the constraint that at most k 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 k = 2 and k = 3, where the result for k = 2 is best possible.