Simultaneous graph embedding with bends and circular arcs
نویسندگان
چکیده
منابع مشابه
Simultaneous Graph Embedding with Bends and Circular Arcs
We consider the problem of simultaneous embedding of planar graphs. We demonstrate how to simultaneously embed a path and an n-level planar graph and how to use radial embeddings for curvilinear simultaneous embeddings of a path and an outerplanar graph. We also show how to use star-shaped levels to find 2-bends per path edge simultaneous embeddings of a path and an outerplanar graph. All embed...
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We consider several variations of the simultaneous embedding problem for planar graphs. We begin with a simple proof that not all pairs of planar graphs have simultaneous geometric embedding. However, using bends, pairs of planar graphs can be simultaneously embedded on the O(n) × O(n) grid, with at most three bends per edge, where n is the number of vertices. The O(n) time algorithm guarantees...
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We consider the problem of simultaneous embedding of planar graphs. There are two variants of this problem, one in which the mapping between the vertices of the two graphs is given and another where the mapping is not given. In particular, we show that without mapping, any number of outerplanar graphs can be embedded simultaneously on an O(n)×O(n) grid, and an outerplanar and general planar gra...
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We prove that there exists a set S of n points in the plane such that every n-vertex planar graph G admits a plane drawing in which every vertex of G is placed on a distinct point of S and every edge of G is drawn as a circular arc.
متن کاملTriangulations with Circular Arcs
An important objective in the choice of a triangulation is that the smallest angle becomes as large as possible. In the straight line case, it is known that the Delaunay triangulation is optimal in this respect. We propose and study the concept of a circular arc triangulation— a simple and effective alternative that offers flexibility for additionally enlarging small angles—and discuss its appl...
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2009
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2008.05.003