License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2018.23
URN: urn:nbn:de:0030-drops-87364
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8736/
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Chan, Timothy M.

Tree Drawings Revisited

pdf-format:
LIPIcs-SoCG-2018-23.pdf (0.6 MB)

Abstract

We make progress on a number of open problems concerning the area requirement for drawing trees on a grid. We prove that
1) every tree of size n (with arbitrarily large degree) has a straight-line drawing with area n2^{O(sqrt{log log n log log log n})}, improving the longstanding O(n log n) bound;
2) every tree of size n (with arbitrarily large degree) has a straight-line upward drawing with area n sqrt{log n}(log log n)^{O(1)}, improving the longstanding O(n log n) bound;
3) every binary tree of size n has a straight-line orthogonal drawing with area n2^{O(log^*n)}, improving the previous O(n log log n) bound by Shin, Kim, and Chwa (1996) and Chan, Goodrich, Kosaraju, and Tamassia (1996);
4) every binary tree of size n has a straight-line order-preserving drawing with area n2^{O(log^*n)}, improving the previous O(n log log n) bound by Garg and Rusu (2003);
5) every binary tree of size n has a straight-line orthogonal order-preserving drawing with area n2^{O(sqrt{log n})}, improving the O(n^{3/2}) previous bound by Frati (2007).

BibTeX - Entry

@InProceedings{chan:LIPIcs:2018:8736,
  author =	{Timothy M. Chan},
  title =	{{Tree Drawings Revisited}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{23:1--23:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-066-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{99},
  editor =	{Bettina Speckmann and Csaba D. T{\'o}th},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8736},
  URN =		{urn:nbn:de:0030-drops-87364},
  doi =		{10.4230/LIPIcs.SoCG.2018.23},
  annote =	{Keywords: graph drawing, trees, recursion}
}

Keywords: graph drawing, trees, recursion
Collection: 34th International Symposium on Computational Geometry (SoCG 2018)
Issue Date: 2018
Date of publication: 08.06.2018

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