The tight bound of first fit decreasing bin-packing algorithm is FFD(I) ≤ 11/9OPT(I) + 6/9

Authors:
György Dósa
Affiliations:
Department of Mathematics, University of Pannonia, Veszprém, Hungary
Venue:
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
Year:
2007

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Abstract

First Fit Decreasing is a classical bin packing algorithm: the items are ordered into their nonincreasing order, and then in this order the next item is always packed into the first bin where it fits. For an instance I let FFD(I) and OPT(I) denote the number of the used bins by algorithm FFD, and an optimal algorithm, respectively. We show in this paper that FFD(I) ≤ 11/9OPT(I) + 6/9, (1) and that this bound is tight. The tight bound of the additive constant was an open question for many years.