Bounded-Degree Spanners in the Presence of Polygonal Obstacles

Abstract

Let V be a finite set of vertices in the plane and S be a finite set of polygonal obstacles. We show how to construct a plane 2-spanner of the visibility graph of V with respect to S. As this graph can have unbounded degree, we modify it in three easy-to-follow steps, in order to bound the degree to 7 at the cost of slightly increasing the spanning ratio to 6.