Improved Space for Bounded-Space, On-Line Bin-Packing

The author presents a sequence of linear-time, bounded-space, on-line, bin-packing algorithms that are based on the “HARMONIC” algorithms ${\text{H}}_k $ introduced by Lee and Lee [J. Assoc. Comput. Mach., 32 (1985), pp. 562–572]. The algorithms in this paper guarantee the worst case performance of ${\text{H}}_k $, whereas they only use $O ( \log \log k )$ instead of k active bins. For $k\geqq 6$, the algorithms in this paper outperform all known heuristics using k active bins. For example, the author gives an algorithm that has worst case ratio less than 17/10 and uses only six active bins.