On Computing the Centroid of the Vertices of an Arrangement and Related Problems

We consider the problem of computing the centroid of all the vertices in a non-degenerate arrangement of n lines. The trivial approach requires the enumeration of all `n 2 ´ vertices. We present an O(n log2 n) algorithm for computing this centroid. For arrangements of n segments we give an O(n 4 3 + ) algorithm for computing the centroid of its vertices. For the special case that all the segments of the arrangement are chords of a simply connected planar region we achieve an O(n log5 n) time bound. Our bounds also generalize to certain natural weighted versions of those problems.

• Type: Conference
• Year: 2007
• Where: WADS
• Authors: Deepak Ajwani, Saurabh Ray, Raimund Seidel, Hans Raj Tiwary
• Keywords: Algorithms, Centroid, Non-degenerate Arrangement, Trivial Approach, WADS 2007