Improved constants for bounded-aspect-ratio rectangle packing

Improve the constants in the asymptotic competitive-ratio upper and lower bounds for online packing nonrotatable rectangles of maximum aspect ratio κ under Tetris-and-gravity constraints.

Background

The paper extends the asymmetric slot-routing framework from squares to rectangles whose aspect ratios are bounded by κ. It proves an O(κ) upper bound and an Ω(κ) lower bound, thereby determining the optimal order of dependence on κ.

Although the asymptotic growth rate is settled, the constants in the upper and lower bounds do not match. The paper explicitly identifies tightening these constants as an unresolved problem.