Morphing Contact Representations of Graphs

Angelini, Patrizio; Chaplick, Steven; Cornelsen, Sabine; Da Lozzo, Giordano; Roselli, Vincenzo

Morphing Contact Representations of Graphs

Dateien

Angelini_2-zrihd4nlcfc35.pdfGröße: 968.33 KBDownloads: 24

Datum

2019

Autor:innen

Angelini, Patrizio

Chaplick, Steven

Cornelsen, Sabine

Da Lozzo, Giordano

Roselli, Vincenzo

Open Access-Veröffentlichung

Open Access Bookpart

Sammlungen

Informatik und Informationswissenschaft

Publikationstyp

Beitrag zu einem Konferenzband

Publikationsstatus

Published

Erschienen in

BAREQUET, Gill, ed., Yusu WANG, ed.. 35th International Symposium on Computational Geometry (SoCG 2019). Wadern: Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. LIPIcs : Leibniz International Proceedings in Informatics. 129. eISSN 1868-8969. Available under: doi: 10.4230/LIPIcs.SoCG.2019.10

Zusammenfassung

We consider the problem of morphing between contact representations of a plane graph. In a contact representation of a plane graph, vertices are realized by internally disjoint elements from a family of connected geometric objects. Two such elements touch if and only if their corresponding vertices are adjacent. These touchings also induce the same embedding as in the graph. In a morph between two contact representations we insist that at each time step (continuously throughout the morph) we have a contact representation of the same type. We focus on the case when the geometric objects are triangles that are the lower-right half of axis-parallel rectangles. Such RT-representations exist for every plane graph and right triangles are one of the simplest families of shapes supporting this property. Thus, they provide a natural case to study regarding morphs of contact representations of plane graphs. We study piecewise linear morphs, where each step is a linear morph moving the endpoints of each triangle at constant speed along straight-line trajectories. We provide a polynomial-time algorithm that decides whether there is a piecewise linear morph between two RT-representations of a plane triangulation, and, if so, computes a morph with a quadratic number of linear morphs. As a direct consequence, we obtain that for 4-connected plane triangulations there is a morph between every pair of RT-representations where the ``top-most'' triangle in both representations corresponds to the same vertex. This shows that the realization space of such RT-representations of any 4-connected plane triangulation forms a connected set.

Fachgebiet (DDC)

004 Informatik

Konferenz

35th International Symposium on Computational Geometry (SoCG 2019), 18. Juni 2019 - 21. Juni 2019, Portland, United States

Zitieren

ISO 690

ANGELINI, Patrizio, Steven CHAPLICK, Sabine CORNELSEN, Giordano DA LOZZO, Vincenzo ROSELLI, 2019. Morphing Contact Representations of Graphs. 35th International Symposium on Computational Geometry (SoCG 2019). Portland, United States, 18. Juni 2019 - 21. Juni 2019. In: BAREQUET, Gill, ed., Yusu WANG, ed.. 35th International Symposium on Computational Geometry (SoCG 2019). Wadern: Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. LIPIcs : Leibniz International Proceedings in Informatics. 129. eISSN 1868-8969. Available under: doi: 10.4230/LIPIcs.SoCG.2019.10

BibTex

@inproceedings{Angelini2019Morph-45596,
  year={2019},
  doi={10.4230/LIPIcs.SoCG.2019.10},
  title={Morphing Contact Representations of Graphs},
  number={129},
  publisher={Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
  address={Wadern},
  series={LIPIcs : Leibniz International Proceedings in Informatics},
  booktitle={35th International Symposium on Computational Geometry (SoCG 2019)},
  editor={Barequet, Gill and Wang, Yusu},
  author={Angelini, Patrizio and Chaplick, Steven and Cornelsen, Sabine and Da Lozzo, Giordano and Roselli, Vincenzo}
}

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