Rectangular Partitions of a Rectilinear Polygon
release_hqwb4tbicfhvrhr5qp5746srci
by
Hwi Kim, Jaegun Lee, Hee-Kap Ahn
2021
Abstract
We investigate the problem of partitioning a rectilinear polygon P with n
vertices and no holes
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^2n)-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^2n)-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.
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