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 Hk 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 Hk, whereas they only use O(log log k) instead ofk active bins. For k >_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 / l0 and uses only six active bins. Key words, combinatorial problems, on-line, bin-packing, suboptimal algorithms AMS subject classifications. 90B35, 90C27