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arXiv · 1411.5455

Generalized $β$-skeletons

Mirosław Kowaluk·Gabriela Majewska
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Abstract

$β$-skeletons, a prominent member of the neighborhood graph family, have interesting geometric properties and various applications ranging from geographic networks to archeology. This paper focuses on developing a new, more general than the present one, definition of $β$-skeletons based only on the distance criterion. It allows us to consider them in many different cases, e.g. for weighted graphs or objects other than points. Two types of $β$-skeletons are especially well-known: the Gabriel Graph (for $β= 1$) and the Relative Neighborhood Graph (for $β= 2$). The new definition retains relations between those graphs and the other well-known ones (minimum spanning tree and Delaunay triangulation). We also show several new algorithms finding $β$-skeletons.

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BibTeXRIS

Mirosław Kowaluk, Gabriela Majewska. 2014-11-20. Generalized $β$-skeletons. https://arxiv.org/abs/1411.5455

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