A simple on-line bin-packing algorithm

The one-dimensional on-line bin-packing problem is considered, A simple <italic>O</italic>(1)-space and <italic>O</italic>(<italic>n</italic>)-time algorithm, called HARMONIC<italic><subscrpt>M</subscrpt></italic>, is presented. It is shown that this algorithm can achieve a worst-case performance ratio of less than 1.692, which is better than that of the <italic>O</italic>(<italic>n</italic>)-space and <italic>O</italic>(<italic>n</italic> log <italic>n</italic>)-time algorithm FIRST FIT. Also shown is that 1.691 … is a lower bound for <italic>all</italic> <italic>0</italic>(1)-space on-line bin-packing algorithms. Finally a revised version of HARMONIC<italic><subscrpt>M </subscrpt></italic>, an <italic>O</italic>(<italic>n</italic>)-space and <italic>O</italic>(<italic>n</italic>)- time algorithm, is presented and is shown to have a worst-case performance ratio of less than 1.636. d