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IPL
2002

Lower bounds for approximate polygon decomposition and minimum gap

13 years 3 months ago
Lower bounds for approximate polygon decomposition and minimum gap
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 (n log n) lower bound on the timecomplexity. 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 (n log n) time. Key words: Lower bounds, Minimum gap, Polygon decomposition, Algebraic decision trees, Computational Geometry
Joachim Gudmundsson, Thore Husfeldt, Christos Levc
Added 22 Dec 2010
Updated 22 Dec 2010
Type Journal
Year 2002
Where IPL
Authors Joachim Gudmundsson, Thore Husfeldt, Christos Levcopoulos
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