Computational geometry: an introduction
Computational geometry: an introduction
Improved bounds for covering general polygons with rectangles
Proc. of the seventh conference on Foundations of software technology and theoretical computer science
Performance guarantees on a sweep-line heuristic for covering rectilinear polygons with rectangles
SIAM Journal on Discrete Mathematics
Minimum partitioning simple rectilinear polygons in O(n log log n) - time
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Triangulating a simple polygon in linear time
Discrete & Computational Geometry
Optimal time bounds for some proximity problems in the plane
Information Processing Letters
Minimum dissection of a rectilinear polygon with arbitrary holes into rectangles
Discrete & Computational Geometry
A New Method of image Compression Using Irreducible Covers of Maximal Rectangles
IEEE Transactions on Software Engineering
Lower bounds for algebraic computation trees
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Optimizing query processing in cache-aware wireless sensor networks
SSDBM'10 Proceedings of the 22nd international conference on Scientific and statistical database management
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We consider the problem of decomposing polygons (with holes) into various types of simpler polygons. We focus on the problem of partitioning a rectilinear polygon, with holes, into rectangles, and show an Ω (n log n) lower bound on the time-complexity. The result holds for any decomposition, optimal or approximative. The bound matches the complexity of a number of algorithms in the literature, proving their optimality and settling the complexity of approximate polygon decomposition in these cases.As a related result we show that any non-trivial approximation algorithm for the minimum gap problem requires Ω (n log n) time.