Corner Sequence

The idea

The Corner Sequence describes a packing as a construction order: blocks enter one at a time, each placed into a corner of the region already built (a concave notch of the current skyline), recorded together with which corner it took. Maintaining the set of available corners as blocks arrive is cheap, so decoding a full sequence is worst-case linear, and, crucially, an annealing move that alters a suffix of the sequence can re-decode only that suffix: the prefix's geometry is untouched.

That incrementality is the representation's reason to exist. Annealers spend nearly all their time evaluating candidate floorplans; a representation that turns most moves into partial re-evaluations multiplies the effective iteration budget without touching the cooling schedule.

Trade-offs

Like the O-tree and B-tree, the corner sequence is confined to the P-admissible world of compacted packings: decode always yields a bottom-left-pushed arrangement, ideal for area but requiring extensions for slack-hungry constraints. Its search space and solution quality are on par with the B-tree family; the differentiation is evaluation speed under long move chains, and a construction viewpoint that some constraint types (place block X in the bottom-left region, keep Y on the boundary) express naturally.

Where you meet it today

In the efficiency-focused corner of the literature and inside packers where evaluation throughput is the bottleneck. Conceptually it also bridges toward online and constructive packing heuristics, since its decode is a constructive packer replayed from a script.