Simultaneous Orthogonal Planarity

Patrizio Angelini; Steven Chaplick; Sabine Cornelsen; Giordano Da Lozzo; Giuseppe Di Battista; Peter Eades; Philipp Kindermann; Jan Kratochvil; Fabian Lipp; and Ignaz Rutter

arXiv · 1608.08427

Simultaneous Orthogonal Planarity

Patrizio Angelini·Steven Chaplick·Sabine Cornelsen·Giordano Da Lozzo·Giuseppe Di Battista·Peter Eades·Philipp Kindermann·Jan Kratochvil·Fabian Lipp·and Ignaz Rutter

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Abstract

We introduce and study the $\textit{OrthoSEFE}-k$ problem: Given $k$ planar graphs each with maximum degree 4 and the same vertex set, do they admit an OrthoSEFE, that is, is there an assignment of the vertices to grid points and of the edges to paths on the grid such that the same edges in distinct graphs are assigned the same path and such that the assignment induces a planar orthogonal drawing of each of the $k$ graphs? We show that the problem is NP-complete for $k \geq 3$ even if the shared graph is a Hamiltonian cycle and has sunflower intersection and for $k \geq 2$ even if the shared graph consists of a cycle and of isolated vertices. Whereas the problem is polynomial-time solvable for $k=2$ when the union graph has maximum degree five and the shared graph is biconnected. Further, when the shared graph is biconnected and has sunflower intersection, we show that every positive instance has an OrthoSEFE with at most three bends per edge.

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BibTeX RIS

Patrizio Angelini, Steven Chaplick, Sabine Cornelsen, Giordano Da Lozzo, Giuseppe Di Battista, Peter Eades, Philipp Kindermann, Jan Kratochvil, Fabian Lipp, and Ignaz Rutter. 2016-08-30. Simultaneous Orthogonal Planarity. https://arxiv.org/abs/1608.08427

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