License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
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DOI: 10.4230/LIPIcs.FSTTCS.2017.8
URN: urn:nbn:de:0030-drops-84043
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8404/
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Agarwal, Pankaj K. ; Fox, Kyle ; Nath, Abhinandan

Maintaining Reeb Graphs of Triangulated 2-Manifolds

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LIPIcs-FSTTCS-2017-8.pdf (0.6 MB)

Abstract

Let M be a triangulated, orientable 2-manifold of genus g without boundary, and let h be a height function over M that is linear within each triangle. We present a kinetic data structure (KDS) for
maintaining the Reeb graph R of h as the heights of M's vertices vary continuously with time. Assuming the heights of two vertices of M become equal only O(1) times, the KDS processes O((k + g) n \polylog n) events; n is the number of vertices in M, and k is the number of external events which change the combinatorial structure of R. Each event is processed in O(\log^2 n) time, and the total size of our KDS is O(gn). The KDS can be extended to maintain an augmented Reeb graph as well.

BibTeX - Entry

@InProceedings{agarwal_et_al:LIPIcs:2018:8404,
  author =	{Pankaj K. Agarwal and Kyle Fox and Abhinandan Nath},
  title =	{{Maintaining Reeb Graphs of Triangulated 2-Manifolds}},
  booktitle =	{37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017)},
  pages =	{8:1--8:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-055-2},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{93},
  editor =	{Satya Lokam and R. Ramanujam},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8404},
  URN =		{urn:nbn:de:0030-drops-84043},
  doi =		{10.4230/LIPIcs.FSTTCS.2017.8},
  annote =	{Keywords: Reeb graphs, 2-manifolds, topological graph theory}
}

Keywords: Reeb graphs, 2-manifolds, topological graph theory
Collection: 37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017)
Issue Date: 2018
Date of publication: 12.02.2018

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