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Sequences of Spanning Trees and a Fixed Tree Theorem

Summary: Sequences of Spanning Trees and a
Fixed Tree Theorem 
Oswin Aichholzer y
Franz Aurenhammer z
Institute for Theoretical Computer Science
Graz University of Technology
Graz, Austria
e-mail: foaich,aureng@igi.tu-graz.ac.at
Ferran Hurtado x
Departament de Matematica Aplicada II
Universitat Politecnica de Catalunya
Barcelona, Spain
e-mail: hurtado@ma2.upc.es
Let T S be the set of all crossing-free spanning trees of a planar n-point set
S. We prove that T S contains, for each of its members T , a length-decreasing
sequence of trees T o ; : : : ; T k such that T o = T , T k = MST (S), T i does not
cross T i 1 for i = 1; : : : ; k, and k = O(log n). Here MST (S) denotes the
Euclidean minimum spanning tree of the point set S.
As an implication, the number of length-improving and planar edge moves


Source: Aurenhammer, Franz - Institute for Theoretical Computer Science, Technische Universitšt Graz
Technische Universitšt Graz, Institute for Software Technology


Collections: Computer Technologies and Information Sciences