Improved bounds for rectangular and guillotine partitions†

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We study the problem of partitioning a rectangle S with a set of interior points Q intorectangles by introducing a set of line segments of least total length. The set of partitioning line segments must include every point in Q. Since this problem is computationally intractable (NP-hard), several approximation algorithms for its solution have been developed. In this paper we show that the legnth of an optimal guillotine partition is not greater than 1.75 times the length of an optimal rectangular partition. Since an optimal guillotine partition can be obtained on O(n5) time, we have a polynomial time approximation algorithm for finding near-optimal rectangular partitions.

Keywords

approximation algorithms
partition of rectilinear polygons
polynomial time complexity
guillotine partitions
computational geometry

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†

This research was supported in part by the National Science Foundation under Grant DCR-8503163. Apreliminary version of this paper was presented at the 24th Annual Allerton Conference on Communication, Control and Computing, October 1986.

‡

Professor S.-Q. Zheng's present address is: Department of Computer Science, Louisiana State University,Baton Rouge, LA 70803-4020, USA.

Copyright © 1989 Published by Elsevier Ltd.