A linear-time algorithm solves the maximum-area boundary-anchored rectangle packing problem for sorted points on a square's boundary, plus an O(n^4) algorithm for anchored squares on opposite sides.
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Packing Boundary-Anchored Rectangles and Squares
A linear-time algorithm solves the maximum-area boundary-anchored rectangle packing problem for sorted points on a square's boundary, plus an O(n^4) algorithm for anchored squares on opposite sides.