Mad at Edge Crossings? Break the Edges!
One of the main principles for the effective visualization of graphs is the avoidance of edge crossings. Around this problem, very active research has been performed with works ranging from combinatorics, to algorithmics, visualization effects, to psychological user studies. Recently, the pragmatic approach has been proposed to avoid crossings by drawing the edges only partially. Unfortunately, no formal model and efficient algorithms have been formulated to this end. We introduce the concept for drawings of graphs with partially drawn edges (PED). Therefore we consider graphs with and without given embedding and characterize PEDs with concepts like symmetry and homogeneity. For graphs without embedding we formulate a sufficient condition to guarantee a symmetric homogeneous PED, and identify a nontrivial graph class which has a symmetric homogeneous PED. For graphs with given layout we consider the variants of maximizing the shortest partially drawn edge and the total length respectively.
KeywordsIntersection Point Small Circle Intersection Graph Maximal Match Graph Class
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