Bounded-Degree Spanners in the Presence of Polygonal Obstacles

by   André van Renssen, et al.

Let V be a finite set of vertices in the plane and S be a finite set of polygonal obstacles, where the vertices of S are in V. 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.


page 1

page 2

page 3

page 4


Routing on the Visibility Graph

We consider the problem of routing on a network in the presence of line ...

The number of small-degree vertices in matchstick graphs

A matchstick graph is a crossing-free unit-distance graph in the plane. ...

Computing the obstacle number of a plane graph

An obstacle representation of a plane graph G is V(G) together with a se...

Reducing the maximum degree of a graph: comparisons of bounds

Let λ(G) be the smallest number of vertices that can be removed from a n...

Recognizing Visibility Graphs of Triangulated Irregular Networks

A Triangulated Irregular Network (TIN) is a data structure that is usual...

Visibility Polygons and Visibility Graphs among Dynamic Polygonal Obstacles in the Plane

We devise an algorithm for maintaining the visibility polygon of any que...

Finite degree clones are undecidable

A clone of functions on a finite domain determines and is determined by ...