Tight competitive ratio for the asymmetric square-packing algorithm

Determine whether the asymptotic competitive-ratio upper bound 2.373318506305... for the asymmetric recursive square-packing algorithm with split parameter p*=0.578649053069... is tight, given the algorithm-specific lower bound of 2.

Background

The paper introduces an asymmetric recursive algorithm for online packing axis-parallel squares into a unit-width strip under Tetris-and-gravity constraints. For the optimized split parameter p*, the analysis proves an asymptotic competitive-ratio upper bound of approximately 2.373318506305. A repeated-square construction establishes a lower bound of 2 for the algorithm, leaving a nontrivial gap between the known upper and lower bounds.

The unresolved issue is whether the proven upper bound accurately reflects the algorithm’s true asymptotic competitive ratio, or whether stronger adversarial instances can raise the lower bound, potentially to the upper-bound value.