Enumerating floorplans with walls

Let P be a set of n points in the proper inside of an axis-aligned rectangle R, and each point in P has a type, which is h-type, v-type, or f-type. Those are shortened forms of horizontal type, vertical type, and free type. We wish to dissect R into a set S of n + 1 rectangles by n horizontal or vertical line segments so that each point in P is on the common boundary line segment between two rectangles in S, and also each h-type point in P is on a horizontal line segment, each v-type point in P is on a vertical line segment, and each f-type point in P is on a horizontal or vertical line segment. Such a dissection of R is called a feasible floorplan of R with respect to P. Each point in P corresponds to the location of a structurally necessary horizontal or vertical wall, or a column (pillar) to support the upper part. In this paper, when P consists of points of the three described types, we present an efficient algorithm that enumerates all the feasible floorplans of R with respect to P. The algorithm is based on the reverse search method and enumerates all the feasible floorplans in O(n |SP |) time using O(n2) space, after O(n log n) time preprocessing, where SP is the set of the feasible floorplans of R with respect to P. Moreover, we show that, after O(n log n) time preprocessing, one can enumerate all feasible floorplans in SP in O(n) delay using O(n2) space.(c) 2023 Elsevier B.V. All rights reserved.