Abstract
Consider the classic bin packing problem, in which we seek to pack a list of items into the minimum number of unit-capacity bins. The worst-case performance of a compound bin packing algorithm that selects the better packing produced by two previously analyzed heuristics, namely, FFD (first fit decreasing) and B2F (best two fit) is investigated. FFD and B2F can asymptotically require as many as $\frac{11}{9}$ and $\frac{5}{4}$ times the optimal number of bins, respectively. A new technique, weighting function averaging, is introduced to prove that our compound algorithm is superior to the individual heuristics on which it is based, never using more than $\frac{6}{5}$ times the optimal number of bins.
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