Closed on-line bin packing
AbstractAn optimal algorithm for the classical bin packing problem partitions (packs) a given set of items with sizes at most 1 into a smallest number of unit-capacity bins such that the sum of the sizes of the items in each bin is at most 1. Approximation algorithms for this NP-hard problem are called on-line if the items are packed sequentially into bins with the bin receiving a given item being independent of the number and sizes of all items as yet unpacked. Off-line algorithms plan packings assuming full (advance) knowledge of all item sizes. The closed on-line algorithms are intermediate: item sizes are not known in advance but the number n of items is. The uniform model, where the n item sizes are independent uniform random draws from [0,1], commands special attention in the average-case analysis of bin packing algorithms. In this model, the expected wasted space produced by an optimal off-line algorithm is Θ(√n), while that produced by an optimal on-line algorithm is Θ(√n log n)- Surprisingly, an optimal closed on-line algorithm also wastes only s Θ(√n) space on the average. A proof of this last result is the principal contribution of this paper. However, we also identify a class of optimal closed algorithms, extend the main result to other probability models, and give an estimate of the hidden constant factor.
Download data is not yet available.
How to Cite
Asgeirsson, E. I. (2002). Closed on-line bin packing. Acta Cybernetica, 15(3), 361-367. Retrieved from https://cyber.bibl.u-szeged.hu/index.php/actcybern/article/view/3585