Rectangular Partitions of a Rectilinear Polygon

Abstract

We investigate the problem of partitioning a rectilinear polygon P with n vertices and no holes into rectangles using disjoint line segments drawn inside P under two optimality criteria. In the minimum ink partition, the total length of the line segments drawn inside P is minimized. We present an O(n 3 )-time algorithm using O(n 2 ) space that returns a minimum ink partition of P . In the thick partition, the minimum side length over all resulting rectangles is maximized. We present an O(n 3 log 2 n)-time algorithm using O(n 3 ) space that returns a thick partition using line segments incident to vertices of P , and an O(n 6 log 2 n)-time algorithm using O(n 6 ) space that returns a thick partition using line segments incident to the boundary of P . We also show that if the input rectilinear polygon has holes, the corresponding decision problem for the thick partition problem using line segments incident to vertices of the polygon is NP-complete. We also present an O(m 3 )time 3-approximation algorithm for the minimum ink partition for a rectangle containing m point holes.