Better bounds on the union complexity of locally fat objects

We prove that the union complexity of a set of n constantcomplexity locally fat objects (which can be curved and/or non-convex) in the plane is O(λt+2(n) log n), where t is the maximum number of times the boundaries of any two objects intersect. This improves the previously best known bound by a logarithmic factor. Categories and Subject Descriptors F.2 [Theory of Computation]: Analysis of Algorithms and Problem Complexity General Terms Algorithms, Theory. Keywords Combinatorial geometry, union complexity, fat objects.

• Type: Conference
• Year: 2010
• Where: COMPGEOM
• Authors: Mark de Berg
• Keywords: COMPGEOM 2010, Complexity General Terms, Fat Objects, Union Complexity