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Morphing Graph Drawings in the Presence of Point Obstacles (2311.14516v1)
Published 24 Nov 2023 in cs.CG
Abstract: A crossing-free morph is a continuous deformation between two graph drawings that preserves straight-line pairwise noncrossing edges. Motivated by applications in 3D morphing problems, we initiate the study of morphing graph drawings in the plane in the presence of stationary point obstacles, which need to be avoided throughout the deformation. As our main result, we prove that it is NP-hard to decide whether such an obstacle-avoiding 2D morph between two given drawings of the same graph exists. This is in sharp contrast to the classical case without obstacles, where there is an efficiently verifiable (necessary and sufficient) criterion for the existence of a morph.
- Convexifying polygons without losing visibilities. In G. Aloupis and Bremner, editors, CCCG, pages 229–234, 2011. URL: http://www.cccg.ca/proceedings/2011/papers/paper70.pdf.
- How to morph planar graph drawings. SIAM J. Comput., 46(2):824–852, 2017. doi:10.1137/16M1069171.
- Optimal morphs of convex drawings. In L. Arge and J. Pach, editors, SoCG, volume 34 of LIPIcs, pages 126–140. Schloss Dagstuhl – Leibniz-Zentrum für Informatik, 2015. doi:10.4230/LIPIcs.SOCG.2015.126.
- Pole dancing: 3D morphs for tree drawings. J. Graph Algorithms Appl., 23(3):579–602, 2019. doi:10.7155/jgaa.00503.
- Morphing tree drawings in a small 3D grid. J. Graph Algorithms Appl., 27(4):241–279, 2023. doi:10.7155/jgaa.00623.
- Morphing planar graph drawings through 3D. In L. Gąsieniec, editor, SOFSEM, volume 13878 of LNCS, pages 80–95. Springer, 2023. doi:10.1007/978-3-031-23101-8_6.
- S. Cairns. Deformations of plane rectilinear complexes. Amer. Math. Monthly, 51(5):247–252, 1944.
- Straightening polygonal arcs and convexifying polygonal cycles. Discrete Comput. Geom., 30:205–239, 2003. doi:10.1007/s00454-003-0006-7.
- Upward planar morphs. Algorithmica, 82(10):2985–3017, 2020. doi:10.1007/s00453-020-00714-6.
- Warping & Morphing of Graphical Objects. Morgan Kaufmann, 1999.
- Convexity-increasing morphs of planar graphs. Comput. Geom., 84:69–88, 2019. doi:10.1016/j.comgeo.2019.07.007.
- B. Klemz. Convex drawings of hierarchical graphs in linear time, with applications to planar graph morphing. In P. Mutzel, R. Pagh, and G. Herman, editors, ESA, volume 204 of LIPIcs, pages 57:1–57:15. Schloss Dagstuhl – Leibniz-Zentrum für Informatik, 2021. doi:10.4230/LIPIcs.ESA.2021.57.
- How important is the “mental map”? – An empirical investigation of a dynamic graph layout algorithm. In M. Kaufmann and D. Wagner, editors, GD, volume 4372 of LNCS, pages 184–195. Springer, 2006. doi:10.1007/978-3-540-70904-6_19.
- C. Thomassen. Deformations of plane graphs. J. Combin. Theory Ser. B, 34(3):244–257, 1983. doi:10.1016/0095-8956(83)90038-2.