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arXiv · 1907.13558

Level-Planar Drawings with Few Slopes

Guido Brückner·Nadine Davina Krisam·Tamara Mchedlidze
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Abstract

We introduce and study level-planar straight-line drawings with a fixed number $\lambda$ of slopes. For proper level graphs, we give an $O(n \log^2 n / \log \log n)$-time algorithm that either finds such a drawing or determines that no such drawing exists. Moreover, we consider the partial drawing extension problem, where we seek to extend an immutable drawing of a subgraph to a drawing of the whole graph, and the simultaneous drawing problem, which asks about the existence of drawings of two graphs whose restrictions to their shared subgraph coincide. We present $O(n^{4/3} \log n)$-time and $O({\lambda} n^{10/3} \log n)$-time algorithms for these respective problems on proper level-planar graphs. We complement these positive results by showing that testing whether non-proper level graphs admit level-planar drawings with $\lambda$ slopes is $\textsf{NP}$-hard even in restricted cases.

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Guido Brückner, Nadine Davina Krisam, Tamara Mchedlidze. 2019-07-31. Level-Planar Drawings with Few Slopes. https://arxiv.org/abs/1907.13558

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