Level-Planar Drawings with Few Slopes [article]

Guido Brückner, Nadine Davina Krisam, Tamara Mchedlidze
2019 arXiv   pre-print
We introduce and study level-planar straight-line drawings with a fixed number λ of slopes. For proper level graphs, we give an O(n log^2 n / loglog 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
more » ... trictions to their shared subgraph coincide. We present O(n^4/3log n)-time and O(λ n^10/3log 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 λ slopes is NP-hard even in restricted cases.
arXiv:1907.13558v1 fatcat:a6mtdmeqgfdbvlmvgjn4nm323y