Square Tree, or How To Pack 200 X-mas Trees
Distributed Geometric Packing via Crystallographic Lattices.
SquareTree is a scalable computational geometry engine for solving hard non-convex packing problems, inspired by the Santa 2025 Challenge. Its core advantage is speed: instead of spending compute on slow, chaotic exploration, it uses geometric structure to reach near-optimal configurations remarkably quickly.
We utilize a Modified Sparrow Search Algorithm (SSA) adapted specifically for fixed-dimension square bins. While the original Sparrow heuristic ( Gardeyn et al. ) excels at strip packing (minimizing infinite length) via random initialization, our engine introduces a “Seeded Crystal” capability. Rather than beginning with high-entropy random placement, the solver accepts a pre-loaded, geometrically derived lattice structure. This allows the optimization pipeline to bypass the chaotic “cold start” phase and immediately focus on high-density relaxation.
The result is a packing engine designed for scalable performance - finding excellent solutions fast, with fixed compute budget, and making difficult geometric search practical at larger problem sizes (for example, packing 1000s non-convex shapes with deep caves, similar to above).