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An Integer-Linear Program for Bend-Minimization in Ortho-Radial Drawings
arXiv - CS - Computational Geometry Pub Date : 2020-08-24 , DOI: arxiv-2008.10373 Benjamin Niedermann, Ignaz Rutter
arXiv - CS - Computational Geometry Pub Date : 2020-08-24 , DOI: arxiv-2008.10373 Benjamin Niedermann, Ignaz Rutter
An ortho-radial grid is described by concentric circles and straight-line
spokes emanating from the circles' center. An ortho-radial drawing is the
analog of an orthogonal drawing on an ortho-radial grid. Such a drawing has an
unbounded outer face and a central face that contains the origin. Building on
the notion of an ortho-radial representation (Barth et al., SoCG, 2017), we
describe an integer-linear program (ILP) for computing bend-free ortho-radial
representations with a given embedding and fixed outer and central face. Using
the ILP as a building block, we introduce a pruning technique to compute
bend-optimal ortho-radial drawings with a given embedding and a fixed outer
face, but freely choosable central face. Our experiments show that, in
comparison with orthogonal drawings using the same embedding and the same outer
face, the use of ortho-radial drawings reduces the number of bends by 43.8% on
average. Further, our approach allows us to compute ortho-radial drawings of
embedded graphs such as the metro system of Beijing or London within seconds.
更新日期：2020-08-26
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