The Best-Fit Rule for Multibin Packing: An Extension of Graham's List Algorithms
Résumé
In this paper, we deal with multibin packing problems. These problems are linked to multiprocessor-task scheduling as well as to bin packing problems: they consist of n objects to be packed into m bins, with each object requiring space in several bins. We propose an intuitive greedy approach (the best-fit rule), which extends the well-known list algorithms for multiprocessor scheduling, to solve the case when objects have fixed height and size. We prove that it provides a 2-approximation, and even a 4/3-approximation if the objects are sorted by non-increasing heights. Based on this method, a polynomial time approximation scheme (PTAS) will be developed.