On‐line bin packing with restricted repacking

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.