Enumerating Floorplans with Aligned Columns - NAKANO, Shin-ichi (IEICE Transactions on Information and Systems, 2025)
A floorplan is a partition of an axis-aligned rectangle into a set of smaller rectangles. Given an axis-aligned rectangle R and a set P of points in R we wish to partition R into a set S of rectangles so that each point in P is on a boundary of a rectangle in S. We call such a partition of R a floorplan covering P. Intuitively P is the locations of columns and a floorplan covering P is a floorplan in which no column is in the proper inside of a room and each column is on a wall. In this paper we design an algorithm to generate all floorplans covering P when P is the set of given grid points. The algorithm generates each floorplan in O(|P|) time.