Bin Packing with Discrete Item SizesPart II : Average - Case Behavior of FFD and BFDE
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Bin Packing with Discrete Item Sizes, Part I: Perfect Packing Theorems and the Average Case Behavior of Optimal Packings
We consider the one-dimensional bin packing problem with unit-capacity bins and item sizes chosen according to the discrete uniform distribution Ufj; kg, 1 < j k; where each item size in f1=k; 2=k; : : : ; j=kg has probability 1=j of being chosen. Note that for xed j; k as m ! 1 the discrete distributions Ufmj; mkg approach the continuous distribution U(0; j=k], where the item sizes are chosen ...
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We consider the one-dimensional bin packing problem under the discrete uniform distributions U{j, k}, 1 ≤ j ≤ k − 1, in which the bin capacity is k and item sizes are chosen uniformly from the set {1, 2, . . . , j}. Note that for 0 < u = j/k ≤ 1 this is a discrete version of the previously studied continuous uniform distribution U(0, u], where the bin capacity is 1 and item sizes are chosen uni...
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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...
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Bin covering takes as input a list of item sizes and places them into bins of unit demand so as to maximize the number of bins whose demand is satissed. This is in a sense a dual problem to the classical one-dimensional bin packing problem, but has for many years lagged behind the latter as far as the quality of the best approximation algorithms. We design algorithms for this problem that close...
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We consider the one-dimensional bin packing problem with unit-capacity bins and item sizes chosen according to the discrete uniform distribution Ufj; kg, 1 < j k; where each item size in f1=k; 2=k; : : :; j=kg has probability 1=j of being chosen. Note that for xed j; k as m ! 1 the discrete distributions Ufmj; mkg approach the continuous distribution U(0; j=k], where the item sizes are chosen u...
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