Continuous Yao graphs

摘要

In this paper, we introduce a variation of the well-studied Yao graphs. Given a set of points S subset of 1182 and an angle 0 < 8 <= 2 pi, we define the continuous Yao graph cY(theta) with vertex set S and angle theta as follows. For each p, q is an element of S, we add an edge from p to q in cY(theta) if there exists a cone with apex p and aperture theta such that q is a closest point to p inside this cone.