Resource augmented semi-online bounded space bin packing
Discrete Applied Mathematics
A robust APTAS for the classical bin packing problem
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
On-line bin packing with restricted repacking
Journal of Combinatorial Optimization
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The typical online bin-packing problem requires the fitting of a sequence of rationals in (0,1] into a minimum number of bins of unit capacity, by packing the ith input element without any knowledge of the sizes or the number of input elements that follow. Moreover, unlike typical online problems, this one issue does not admit any data reorganization, i.e., no element can be moved from one bin to another. In this paper, first of all, the "Relaxed" online bin-packing model will be formalized; this model allows a constant number of elements to move from one bin to another, as a consequence of the arrival of a new input element. Then, in the context of this new model, two online algorithms will be described. The first presents linear time and space complexities with a 1.5 approximation ratio and moves, at most once, only "small" elements; the second, instead, is an O(n log n) time and linear space algorithm with a 1.33. . . approximation ratio and moves each element a constant number of times. In the worst case, as a result of the arrival of a new input element, the first algorithm moves no more than three elements, while the second moves as many as seven elements. Please note that the number of movements performed is explicitly considered in the complexity analysis. Both algorithms are below the theoretical 1.536. . . lower bound, effective for the online bin-packing algorithms without the movement of elements. Moreover, our algorithms are "more online" than any other linear space online bin-packing algorithm because, unlike the algorithms already known, they allow the return of a (possibly relevant) fraction of bins before the work is carried out.