Improved Upper Bounds for Dynamic Bin Packing of General, Unit-Fraction, and Power-Fraction Squares

This paper presents significant upper-bound improvements for dynamic 2D square bin packing, where square items arrive and depart over time and the objective is to minimize the peak number of concurrent active unit bins. In our model, repacking is permitted only within a destination bin upon item arrival; migration between active bins is strictly forbidden. By introducing a streamlined two-list algorithm and proving a tight $5\mathrm{/}16$ occupied-area bound for Next-Fit Decreasing Height, we reduce the upper bound on the asymptotic competitive ratio for arbitrary squares from 4.2154 down to 3.918, breaking a longstanding theoretical ceiling. For restricted variants, we establish asymptotic competitive ratios of at most 3.356 for unit-fraction side lengths and 2.211 for power-fraction side lengths.