Floorplans with Walls

Abstract

Let P be a set of n points in the proper inside of an axis-aligned rectangle R, and each point in P is either h-type, v-type or f-type. We wish to partition R into a set S of rectangles by n 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 and each v-type point in P is on a vertical line segment. (Each f-type point in P is on a line segment. f-type menas free type). Such a partition 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 upper part, and a feasible floorplan is a floorplan achieving suitable earthquake resistance. An algorithm to enumerate all feasible floorplans of R with respect to P is known when P consists of only f-type points. In this paper when P consists of the three type points we give an efficient algorithm to enumerate all feasible floorplans of R with respect to P. The algorithm is based on the reverse search method, and enumerates all feasible floorplans in time using O(n) space, after time preprocessing, where is the set of the feasible floorplans of R with respect to P.