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Sloginsky drawings of graphs

In this paper we combine the recently introduced slanted orthogonal (for short: slog) model with the traditional Kandinsky approach into the new Sloginsky model. The slog model introduces diagonal segments into orthogonal drawings and restricts crossings exclusively to these diagonal segments. Additionally, the traditional 90° bends of orthogonal drawings are replaced by so called half-bends. While the slog model is restricted to graphs of maximum vertex degree four, the Kandinsky model allows arbitrary vertex degree. By combining the two approaches we can profit from the advantages of both models, namely arbitrary vertex degree and increased readability. Since we seek drawings of non-planar graphs, we adopt the topology-shape-metrics (TSM) approach. Motivated by a recent complexity result that shows that the problem of minimizing the total number of bends is NP-hard even for plane graphs [1], we give an ILP formulation that results in Sloginsky drawings that are optimal in terms of the total number of bends. We also perform experiments and discuss properties of the new model.