%0 Conference Paper %1 accddekklr-sop-gd16 %A Angelini, Patrizio %A Chaplick, Steven %A Cornelse, Sabine %A Lozzo, Giordano Da %A Battista, Giuseppe Di %A Eades, Peter %A Kindermann, Philipp %A Kratochvíl, Jan %A Lipp, Fabian %A Rutter, Ignaz %B Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD'16) %D 2016 %E Hu, Yifan %E Nöllenburg, Martin %I Springer-Verlag %K myown orthogonal simultaneous %P 532--545 %R 10.1007/978-3-319-50106-2_41 %T Simultaneous Orthogonal Planarity %V 9801 %X We introduce and study the OrthoSEFE-$k$ problem: Given $k$ planar graphs each with maximum degree 4 and the same vertex set, 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 $k 3$ even if the shared graph is a Hamiltonian cycle and has sunflower intersection and for $k 2$ 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-$k$ with at most three bends per edge.

@inproceedings{accddekklr-sop-gd16, abstract = {We introduce and study the OrthoSEFE-$k$ problem: Given $k$ planar graphs each with maximum degree 4 and the same vertex set, 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-$k$ with at most three bends per edge.}, added-at = {2016-12-05T15:10:08.000+0100}, arxiv = {https://arxiv.org/abs/1608.08427}, author = {Angelini, Patrizio and Chaplick, Steven and Cornelse, Sabine and Lozzo, Giordano Da and Battista, Giuseppe Di and Eades, Peter and Kindermann, Philipp and Kratochv{\'i}l, Jan and Lipp, Fabian and Rutter, Ignaz}, biburl = {https://www.bibsonomy.org/bibtex/2d5565d307169ad4b65f26c171afd00ac/kindermann}, booktitle = {Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD'16)}, doi = {10.1007/978-3-319-50106-2_41}, editor = {Hu, Yifan and N{\"o}llenburg, Martin}, interhash = {c742b9f42b9587b272aab51d1c0f817f}, intrahash = {d5565d307169ad4b65f26c171afd00ac}, keywords = {myown orthogonal simultaneous}, month = sep, pages = {532--545}, publisher = {Springer-Verlag}, series = {Lecture Notes in Computer Science}, slides = {http://www1.pub.informatik.uni-wuerzburg.de/pub/kindermann/slides/2016-gd-orthosefe.pdf}, timestamp = {2018-09-18T07:03:52.000+0200}, title = {Simultaneous Orthogonal Planarity}, volume = 9801, year = 2016 }