A New Point-Location Algorithm and its Practical Efficiency—Comparison with Existing Algorithms

The point-location problem is stated as follows: Given a subdivision of the plane by a straight line planer graph G with n vertices and an arbitrary query point Q, determine which region of the subdivision contains Q. A new practical point-location algorithm is proposed. It has 0(1) search time, O(n) space, and O(n) preprocessing time in the average case. Existing point-location algorithms, as well as the one proposed here, have been implemented in FORTRAN, and their practical efficiencies are investigated by computational experiments on several planar subdivisions defined by graphs with 200-4000 vertices. It is shown that our 0(1) search-time, O(n) space, and O(n) preprocessing-time algorithm is practically the most efficient among the tested algorithms.