On Geometric Spanners of Euclidean and Unit Disk Graphs

We consider the problem of constructing bounded-degree planar geometric spanners of Euclidean and unit-disk graphs. It is well known that the Delaunay subgraph is a planar geometric spanner with stretch factor Cdel 2.42; however, its degree may not be bounded. Our first result is a very simple linear time algorithm for constructing a subgraph of the Delaunay graph with stretch factor = 1 + 2(k cos k )-1 and degree bounded by k, for any integer parameter k 14. This result immediately implies an algorithm for constructing a planar geometric spanner of a Euclidean graph with stretch factor

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Iyad A. Kanj, Ljubomir Perkovic
• Keywords: CORR 2008, Education, Integer Parameter, Planar Geometric Spanner, Stretch Factor