On Turn-Regular Orthogonal Representations

Michael A. Bekos; Carla Binucci; Giuseppe Di Battista; Walter Didimo; Martin Gronemann; Karsten Klein; Maurizio Patrignani; Ignaz Rutter

arXiv · 2008.09002

On Turn-Regular Orthogonal Representations

Michael A. Bekos·Carla Binucci·Giuseppe Di Battista·Walter Didimo·Martin Gronemann·Karsten Klein·Maurizio Patrignani·Ignaz Rutter

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Abstract

An interesting class of orthogonal representations consists of the so-called turn-regular ones, i.e., those that do not contain any pair of reflex corners that "point to each other" inside a face. For such a representation H it is possible to compute in linear time a minimum-area drawing, i.e., a drawing of minimum area over all possible assignments of vertex and bend coordinates of H. In contrast, finding a minimum-area drawing of H is NP-hard if H is non-turn-regular. This scenario naturally motivates the study of which graphs admit turn-regular orthogonal representations. In this paper we identify notable classes of biconnected planar graphs that always admit such representations, which can be computed in linear time. We also describe a linear-time testing algorithm for trees and provide a polynomial-time algorithm that tests whether a biconnected plane graph with "small" faces has a turn-regular orthogonal representation without bends.

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Michael A. Bekos, Carla Binucci, Giuseppe Di Battista, Walter Didimo, Martin Gronemann, Karsten Klein, Maurizio Patrignani, Ignaz Rutter. 2020-08-20. On Turn-Regular Orthogonal Representations. https://arxiv.org/abs/2008.09002

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