Fast algorithms for bin packing

摘要

Low-order polynomial time algorithms for near-optimal solutions to the problem of bin packing are studied. The previously analyzed FIRST FIT and BEST FIT packing rules are shown to be members of a more generalized class of packing rules all of which have the same worst case behavior. If the input list is in decreasing order, the worst case behavior of the packing rules in the class is considerably improved and, if not the same for all, at least restricted to a narrow range of possibilities. Finally, after showing that any implementation of a packing rule in the class requires at least 0(n log n) comparisons, we present linear-time approximations to these packing rules whose worst case behavior is as good as that of FIRST FIT under a large variety of restrictions on the input.