Morphing Planar Graph Drawings with Bent Edges
نویسندگان
چکیده
منابع مشابه
Morphing Planar Graph Drawings with Bent Edges
We give an algorithm to morph between two planar drawings of a graph, preserving planarity, but allowing edges to bend. The morph uses a polynomial number of elementary steps, where each elementary step is a linear morph that moves each vertex in a straight line at uniform speed. Although there are planarity-preserving morphs that do not require edge bends, it is an open problem to find polynom...
متن کاملMorphing Planar Graph Drawings
The study of planar graphs dates back to Euler and the earliest days of graph theory. Centuries later came the proofs by Wagner, Fáry and Stein that every planar graph can be drawn with straight line segments for the edges, and the algorithm by Tutte for constructing such straight-line drawings given in his 1963 paper, “How to Draw a Graph”. With more recent attention to complexity issues, this...
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We provide an algorithm for computing a planar morph between any two planar straight-line drawings of any n-vertex plane graph in O(n) morphing steps, thus improving upon the previously best known O(n) upper bound. Further, we prove that our algorithm is optimal, that is, we show that there exist two planar straight-line drawings Γs and Γt of an n-vertex plane graph G such that any planar morph...
متن کاملMorphing Planar Graph Drawings with Unidirectional Moves
Alamdari et al. [1] showed that given two straight-line planar drawings of a graph, there is a morph between them that preserves planarity and consists of a polynomial number of steps where each step is a linear morph that moves each vertex at constant speed along a straight line. An important step in their proof consists of converting a pseudo-morph (in which contractions are allowed) to a tru...
متن کاملMorphing Planar Graph Drawings with a Polynomial Number of Steps
In 1944, Cairns proved the following theorem: given any two straight-line planar drawings of a triangulation with the same outer face, there exists a morph (i.e., a continuous transformation) between the two drawings so that the drawing remains straight-line planar at all times. Cairns’s original proof required exponentially many morphing steps. We prove that there is a morph that consists ofO(...
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ژورنال
عنوان ژورنال: Electronic Notes in Discrete Mathematics
سال: 2008
ISSN: 1571-0653
DOI: 10.1016/j.endm.2008.06.007