Slanted Orthogonal Drawings: Model, Algorithms and Evaluations

We introduce a new model in the context of non-planar orthogonal graph drawing that we call slanted orthogonal graph drawing. While in traditional orthogonal drawings each edge is made of alternating axis-aligned line segments, in slanted orthogonal drawings intermediate diagonal segments on the edges are permitted, which allows for: (a) smoothening the bends of the produced drawing (as they are replaced by pairs of “halfbends”), and, (b) emphasizing the crossings of the drawing (as they always appear at the intersection of two diagonal segments). We present an approach to compute bend-optimal slanted orthogonal representations, an efficient heuristic to compute close-to-optimal slanted orthogonal drawings with respect to the total number of bends in quadratic area, and a corresponding LP formulation, when insisting on bend-optimality. On the negative side, we show that bend-optimal slanted orthogonal drawings may require exponential area. Submitted: December 2013 Reviewed: August 2014 Revised: September 2014 Accepted: November 2014 Final: November 2014 Published: November 2014 Article type: Regular paper Communicated by: G. Liotta This article is based on the preliminary version [M. A. Bekos, M. Kaufmann, R. Krug, S. Näher, V. Roselli, Slanted Orthogonal Drawings, In S. Wismath and A. Wolff editors, Proc. of 21st International Symposium on Graph Drawing (GD2013), LNCS 8242, pp. 244255, 2013]. E-mail addresses: [email protected] (M. A. Bekos) [email protected] (M. Kaufmann) [email protected] (R. Krug) [email protected] (T. Ludwig) [email protected] (S. Näher) [email protected] (V. Roselli) 460 Bekos et al. Slanted Orthogonal Drawings