Practical efficiencies of planar point location algorithms

The planar point location problem is one of the most fundamental problems in computational geometry and stated as follows: Given a straight line planar graph (subdivision) with n vertices and an arbitrary query point Q, determine the region containing Q. Many algorithms have been proposed, and some of them are known to be theoretically optimal O(log n) search time, O(n) space and O(nlogn) processing time). In this paper, we implement several representative algorithms in C, and investigate their practical efficiencies by computational experiments on Voronoi diagram with 2¹⁰ - 2¹⁷ vertices.