منابع مشابه
How to Morph Planar Graph Drawings
Given an n-vertex graph and two straight-line planar drawings of the graph that have the same faces and the same outer face, we show that there is a morph (i.e., a continuous transformation) between the two drawings that preserves straight-line planarity and consists of O(n) steps, which we prove is optimal in the worst case. Each step is a unidirectional linear morph, which means that every ve...
متن کاملA Bent Edge Morph for Planar Graph Drawings
We give an algorithm to morph between two planar graph drawings of a graph, preserving planarity. The morph uses a polynomial number of elementary steps. Each step, is composed of a linear morph or a sequence of two linear morphs allowing a vertex to change direction. The planarity is preserved by allowing edges to bend to avoid collisions with the features of the drawing. This algorithm also p...
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...
متن کاملMorphing Planar Graph Drawings Optimally
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 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...
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ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 2017
ISSN: 0097-5397,1095-7111
DOI: 10.1137/16m1069171