Preprocessing convex polygons using range trees for recognition with few finger probes

Abstract

The problem considered is that of recognizing if a given convex polygon comes from a known collection by applying probes. Existing approaches use a number of probes that is linear in the number of sides of the polygon. The current premise is that probing is expensive, while computing is cheap. Accordingly, a method is proposed that recognizes a polygon from the collection, with high probability, using only a constant number of probes, at the cost of fairly large computing resources, particularly, in setting up and applying a range tree data structure. © Springer-Verlag Berlin Heidelberg 2005.