Fast heuristics for minimum length rectangular partitions of polygons
SCG '86 Proceedings of the second annual symposium on Computational geometry
Bounds for partitioning rectilinear polygons
SCG '85 Proceedings of the first annual symposium on Computational geometry
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
A constant-factor approximation for the k-MST problem in the plane
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Efficient decomposition of polygons into L-shapes with application to VLSI layouts
ACM Transactions on Design Automation of Electronic Systems (TODAES)
Matrix Multiplication on Heterogeneous Platforms
IEEE Transactions on Parallel and Distributed Systems
On the number of rectangular partitions
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
The number of guillotine partitions in d dimensions
Information Processing Letters
On the number of rectangulations of a planar point set
Journal of Combinatorial Theory Series A
An approximation algorithm for dissecting a rectangle into rectangles with specified areas
Discrete Applied Mathematics
The number of guillotine partitions in d dimensions
Information Processing Letters
An upper bound on the number of rectangulations of a point set
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
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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(n^5) time, we have a polynomial time approximation algorithm for finding near-optimal rectangular partitions.