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arXiv · 1308.4291

Morphing Planar Graphs Drawings Efficiently

Patrizio Angelini·Fabrizio Frati·Maurizio Patrignani·Vincenzo Roselli
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Abstract

A morph between two straight-line planar drawings of the same graph is a continuous transformation from the first to the second drawing such that planarity is preserved at all times. Each step of the morph moves each vertex at constant speed along a straight line. Although the existence of a morph between any two drawings was established several decades ago, only recently it has been proved that a polynomial number of steps suffices to morph any two planar straight-line drawings. Namely, at SODA 2013, Alamdari et al.[1] proved that any two planar straight-line drawings of a planar graph can be morphed in O(n^4) steps, while O(n^2) steps suffice if we restrict to maximal planar graphs. In this paper, we improve upon such results, by showing an algorithm to morph any two planar straight-line drawings of a planar graph in O(n^2) steps; further, we show that a morph with O(n) steps exists between any two planar straight-line drawings of a series-parallel graph.

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Patrizio Angelini, Fabrizio Frati, Maurizio Patrignani, Vincenzo Roselli. 2013-08-20. Morphing Planar Graphs Drawings Efficiently. https://arxiv.org/abs/1308.4291

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