We are given a sequence of items that can be packed into m unit size bins. In the classical bin packing problem we x the size of the bins and try to pack the items in the minimum number of such bins. In contrast, in the bin stretching problem we x the number of bins and try to pack the items while stretching the size of the bins as least as possible. We present two on-line algorithms for the bin-stretching problem that guarantee a stretching factor of 5/3 for any number m of bins. We then combine the two algorithms and design an algorithm whose stretching factor is 1:625 for any m. The analysis for the performance of this algorithm is tight. The best lower bound for any algorithm is 4/3 for any m≥2. We note that the bin-stretching problem is also equivalent to the classical scheduling (load balancing) problem in which the value of the makespan (maximum load) is known in advance.
CITATION STYLE
Azar, Y., & Regev, O. (1998). On-line bin-stretching. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1518, pp. 71–81). Springer Verlag. https://doi.org/10.1007/3-540-49543-6_7
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