On-line bin packing with restricted repacking
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- Balogh, J., Békési, J., Galambos, G. et al. J Comb Optim (2014) 27: 115. doi:10.1007/s10878-012-9489-4
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Semi-on-line algorithms for the bin-packing problem allow, in contrast to pure on-line algorithms, the use of certain types of additional operations for each step. Examples include repacking, reordering or lookahead before packing the items. Here we define and analyze a semi-on-line algorithm where for each step at most k items can be repacked, for some positive integer k. We prove that the upper bound for the asymptotic competitive ratio of the algorithm is a decreasing function of k, which tends to 3/2 as k goes to infinity. We also establish lower bounds for this ratio and show that the gap between upper and lower bounds is relatively small.