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Documents authored by He, Xin

Found 2 Possible Name Variants:

He, Xin

Document
DOI: 10.4230/LIPIcs.STACS.2011.141
Compact Visibility Representation of Plane Graphs

Authors: Jiun-Jie Wang and Xin He

Published in: LIPIcs, Volume 9, 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)

Abstract
The visibility representation (VR for short) is a classical representation of plane graphs. It has various applications and has been extensively studied. A main focus of the study is to minimize the size of the VR. It is known that there exists a plane graph $G$ with $n$ vertices where any VR of $G$ requires a grid of size at least (2/3)n x((4/3)n-3) (width x height). For upper bounds, it is known that every plane graph has a VR with grid size at most (2/3)n x (2n-5), and a VR with grid size at most (n-1) x (4/3)n. It has been an open problem to find a VR with both height and width simultaneously bounded away from the trivial upper bounds (namely with size at most c_h n x c_w n with c_h < 1 and c_w < 2$). In this paper, we provide the first VR construction with this property. We prove that every plane graph of n vertices has a VR with height <= max{23/24 n + 2 Ceil(sqrt(n))+4, 11/12 n + 13} and width <= 23/12 n. The area (height x width) of our VR is larger than the area of some of previous results. However, bounding one dimension of the VR only requires finding a good st-orientation or a good dual s^*t^*-orientation of G. On the other hand, to bound both dimensions of VR simultaneously, one must find a good $st$-orientation and a good dual s^*t^*-orientation at the same time, and thus is far more challenging. Since st-orientation is a very useful concept in other applications, this result may be of independent interests.
Cite as

Jiun-Jie Wang and Xin He. Compact Visibility Representation of Plane Graphs. In 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 9, pp. 141-152, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{wang_et_al:LIPIcs.STACS.2011.141,
  author =	{Wang, Jiun-Jie and He, Xin},
  title =	{{Compact Visibility Representation of Plane Graphs}},
  booktitle =	{28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)},
  pages =	{141--152},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-25-5},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{9},
  editor =	{Schwentick, Thomas and D\"{u}rr, Christoph},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2011.141},
  URN =		{urn:nbn:de:0030-drops-30064},
  doi =		{10.4230/LIPIcs.STACS.2011.141},
  annote =	{Keywords: plane graph, plane triangulation, visibility representation, st-orientation}
}

Xin, Cheng

Document
DOI: 10.4230/LIPIcs.SoCG.2018.32
Computing Bottleneck Distance for 2-D Interval Decomposable Modules

Authors: Tamal K. Dey and Cheng Xin

Published in: LIPIcs, Volume 99, 34th International Symposium on Computational Geometry (SoCG 2018)

Abstract
Computation of the interleaving distance between persistence modules is a central task in topological data analysis. For 1-D persistence modules, thanks to the isometry theorem, this can be done by computing the bottleneck distance with known efficient algorithms. The question is open for most n-D persistence modules, n>1, because of the well recognized complications of the indecomposables. Here, we consider a reasonably complicated class called 2-D interval decomposable modules whose indecomposables may have a description of non-constant complexity. We present a polynomial time algorithm to compute the bottleneck distance for these modules from indecomposables, which bounds the interleaving distance from above, and give another algorithm to compute a new distance called dimension distance that bounds it from below.
Cite as

Tamal K. Dey and Cheng Xin. Computing Bottleneck Distance for 2-D Interval Decomposable Modules. In 34th International Symposium on Computational Geometry (SoCG 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 99, pp. 32:1-32:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{dey_et_al:LIPIcs.SoCG.2018.32,
  author =	{Dey, Tamal K. and Xin, Cheng},
  title =	{{Computing Bottleneck Distance for 2-D Interval Decomposable Modules}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{32:1--32:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-066-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{99},
  editor =	{Speckmann, Bettina and T\'{o}th, Csaba D.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2018.32},
  URN =		{urn:nbn:de:0030-drops-87453},
  doi =		{10.4230/LIPIcs.SoCG.2018.32},
  annote =	{Keywords: Persistence modules, bottleneck distance, interleaving distance}
}
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