Abstract
A plane graph is rectilinear planar if it admits an embedding-preserving straight-line drawing where each edge is either horizontal or vertical. We prove that rectilinear planarity testing can be solved in optimal O(n) time for any plane series-parallel graph G with n vertices. If G is rectilinear planar, an embedding-preserving rectilinear planar drawing of G can be constructed in O(n) time. Our result is based on a characterization of rectilinear planar series-parallel graphs in terms of intervals of orthogonal spirality that their components can have, and it leads to an algorithm that can be easily implemented.
Work partially supported by: (i) MIUR, grant 20174LF3T8 “AHeAD: efficient Algorithms for HArnessing networked Data”, (ii) Engineering Dep., Univ. Perugia, grant RICBA19FM: “Modelli, algoritmi e sistemi per la visualizzazione di grafi e reti”.
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Didimo, W., Kaufmann, M., Liotta, G., Ortali, G. (2020). Rectilinear Planarity Testing of Plane Series-Parallel Graphs in Linear Time. In: Auber, D., Valtr, P. (eds) Graph Drawing and Network Visualization. GD 2020. Lecture Notes in Computer Science(), vol 12590. Springer, Cham. https://doi.org/10.1007/978-3-030-68766-3_34
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