Two-Dimensional Rectangle Packing: On-Line Methods and Results

Csirik, J., J.B.G. Frenk and M. LabbC, Two-dimensional rectangle packing: on-line methods and results, Discrete Applied Mathematics 45 (1993) 197-204. The first algorithms for the on-line two-dimensional rectangle packing problem were introduced by Coppersmith and Raghavan. They showed that for a family of heuristics 13/4 is an upper bound for the asymptotic worst-case ratios. We have investigated the Next Fit and the First Fit variants of their method. We proved that the asymptotic worst-case ratio equals 13/4 for the Next Fit variant and that 49/16 is an upper bound of the asymptotic worst-case ratio for the First Fit variant.