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