The spanning ratio of β-Skeletons

In this paper we study the spanning ratio of the βskeletons for β ∈ [0, 2]. Both our upper-bounds and lower-bounds improve the previously best known results [10, 12].

[1]  R. Sokal,et al.  A New Statistical Approach to Geographic Variation Analysis , 1969 .

[2]  D. Matula,et al.  Properties of Gabriel Graphs Relevant to Geographic Variation Research and the Clustering of Points in the Plane , 2010 .

[3]  Godfried T. Toussaint,et al.  The relative neighbourhood graph of a finite planar set , 1980, Pattern Recognit..

[4]  Kenneth J. Supowit,et al.  The Relative Neighborhood Graph, with an Application to Minimum Spanning Trees , 1983, JACM.

[5]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[6]  Jyrki Katajaien,et al.  The region approach for computing relative neighborhood graphs in the L p metric , 1988 .

[7]  David P. Dobkin,et al.  Delaunay graphs are almost as good as complete graphs , 1990, Discret. Comput. Geom..

[8]  Godfried T. Toussaint,et al.  Relative neighborhood graphs and their relatives , 1992, Proc. IEEE.

[9]  Carl Gutwin,et al.  Classes of graphs which approximate the complete euclidean graph , 1992, Discret. Comput. Geom..

[10]  David Eppstein,et al.  The Crust and the beta-Skeleton: Combinatorial Curve Reconstruction , 1998, Graph. Model. Image Process..

[11]  Siu-Wing Cheng,et al.  On beta-skeleton as a subgraph of the minimum weight triangulation , 2001, Theor. Comput. Sci..

[12]  Xiang-Yang Li,et al.  Power efficient and sparse spanner for wireless ad hoc networks , 2001, Proceedings Tenth International Conference on Computer Communications and Networks (Cat. No.01EX495).

[13]  David G. Kirkpatrick,et al.  On the Spanning Ratio of Gabriel Graphs and beta-skeletons , 2002, LATIN.

[14]  David Eppstein.  Beta-skeletons have unbounded dilation , 2002, Comput. Geom..