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Let T S be the set of all crossing-free straight line spanning trees of a planar n-point set S. Consider the graph T S where two members T and T of T S are adjacent if T intersects T only in points of S or in common edges. We prove that the diameter of T S is O(log k), where k denotes the number of convex layers of S. Based on this result, we show that the(More)
Inter-organizational systems have significantly been affected by service-oriented architectures (SOA) and Web services - the state-of-the-art technology to implement SOA. SOA is said to enable quick and inexpensive changes of the IT in order to establish new business partnerships or to reflect changes in existing partnerships. However, current approaches to(More)
This paper studies non-crossing geometric perfect matchings. Two such perfect matchings are compatible if they have the same vertex set and their union is also non-crossing. Our first result states that for any two perfect match-ings M and M of the same set of n points, for some k ∈ O(log n), there is a sequence of perfect matchings M = M 0 , M 1 ,. .. , M(More)
Motivated by the bijection between Schnyder labelings of a plane triangulation and partitions of its inner edges into three trees, we look for binary labelings for quadrangu-lations (whose edges can be partitioned into two trees). Our labeling resembles many of the properties of Schnyder's one for triangulations: Apart from being in bijection with tree(More)
We consider a variation of a problem stated by Erd˝ os and Szekeres in 1935 about the existence of a number f ES (k) such that any set S of at least f ES (k) points in general position in the plane has a subset of k points that are the vertices of a convex k-gon. In our setting the points of S are colored, and we say that a (not necessarily convex) spanned(More)
We propose a novel subdivision of the plane that consists of both convex polygons and pseudo-triangles. This pseudo-convex decomposition is significantly sparser than either convex decompositions or pseudo-triangulations for planar point sets and simple polygons. We also introduce pseudo-convex partitions and coverings. We establish some basic properties(More)