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.MFCS.2016.37
URN: urn:nbn:de:0030-drops-64510
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6451/
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Fan, Chenglin ; Filtser, Omrit ; Katz, Matthew J. ; Zhu, Binhai

On the General Chain Pair Simplification Problem

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LIPIcs-MFCS-2016-37.pdf (0.6 MB)

Abstract

The Chain Pair Simplification problem (CPS) was posed by Bereg et al. who were motivated by the problem of efficiently computing and visualizing the structural resemblance between a pair of protein backbones. In this problem, given two polygonal chains of lengths n and m, the goal is to simplify both of them simultaneously, so that the lengths of the resulting simplifications as well as the discrete Frechet distance between them are bounded. When the vertices of the simplifications are arbitrary (i.e., not necessarily from the original chains), the problem is called General CPS (GCPS).

In this paper we consider for the first time the complexity of GCPS under both the discrete Frechet distance (GCPS-3F) and the Hausdorff distance (GCPS-2H). (In the former version, the quality of the two simplifications is measured by the discrete Fr'echet distance, and in the latter version it is measured by the Hausdorff distance.) We prove that GCPS-3F is polynomially solvable, by presenting an widetilde-O((n+m)^6 min{n,m}) time algorithm for the corresponding minimization problem. We also present an O((n+m)^4) 2-approximation algorithm for the problem. On the other hand, we show that GCPS-2H is NP-complete, and present an approximation algorithm for the problem.

BibTeX - Entry

@InProceedings{fan_et_al:LIPIcs:2016:6451,
  author =	{Chenglin Fan and Omrit Filtser and Matthew J. Katz and Binhai Zhu},
  title =	{{On the General Chain Pair Simplification Problem}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{37:1--37:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-016-3},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{58},
  editor =	{Piotr Faliszewski and Anca Muscholl and Rolf Niedermeier},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6451},
  URN =		{urn:nbn:de:0030-drops-64510},
  doi =		{10.4230/LIPIcs.MFCS.2016.37},
  annote =	{Keywords: chain simplification, discrete Frechet distance, dynamic programming, geometric arrangements, protein structural resemblance}
}

Keywords: chain simplification, discrete Frechet distance, dynamic programming, geometric arrangements, protein structural resemblance
Collection: 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)
Issue Date: 2016
Date of publication: 19.08.2016

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