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 \(n+1\) 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 \(O(|S_P|n)\) time using O(n) space, after \(O(n\log n)\) time preprocessing, where \(S_P\) is the set of the feasible floorplans of R with respect to P.