Review of recent development: Probabilistic behaviour of optical bin-packing solutions

Authors:
Richard Loulou
Affiliations:
Mc Gill University and Université de Grenoble, USA
Venue:
Operations Research Letters
Year:
1984

Citing 2
Cited 0

A Bin Packing Algorithm with Complexity O(n log n) and Performance 1 in the Stochastic Limit

Proceedings on Mathematical Foundations of Computer Science
Approximation algorithms for combinatorial problems

Journal of Computer and System Sciences

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Abstract

The bin-packing problem is studied from a probabilistic view point. It is shown that, when the sizes of the n elements to be packed are drawn independently from a probability distribution F, then the minimum number of bins necessary for the packing of these n elements is asymptotically (a.e.) proportional to n in three cases. In all three cases, the constant of proportionality to n is explicitly given. Furthermore, in two of the cases, a heuristic is described which is asymptotically almost surely closed to the optimal solution.