Floorplans with Columns

Abstract

Given an axis-aligned rectangle R and a set P of n points in the proper inside of R we wish to partition R into a set S of $n+1$ rectangles so that each point in P is on the common boundary between two rectangles in S. We call such a partition of R a feasible floorplan of R with respect to P. Intuitively P is the locations of columns and a feasible floorplan is a floorplan in which no column is in the proper inside of a room, i.e., columns are allowed to be placed only on the partition walls between rooms. In this paper 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 $O(|S_P|)$ time using O(n) space where $S_P$ is the set of the feasible floorplans of R with respect to P, while the known algorithms need either $O(n|S_P|)$ time and O(n) space or $O(\log n |S_P|)$ time and $O(n^3)$ space.