On the general chain pair simplification problem

Chenglin Fan, Omrit Filtser, Matthew J. Katz, Binhai Zhu

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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 Fréchet 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 Fréchet distance (GCPS-3F) and the Hausdorff distance (GCPS-2H). (In the former version, the quality of the two simplifications is measured by the discrete Fréchet distance, and in the latter version it is measured by the Hausdorff distance.) We prove that GCPS-3F is polynomially solvable, by presenting an eO((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.

Original languageEnglish
Title of host publication41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016
EditorsAnca Muscholl, Piotr Faliszewski, Rolf Niedermeier
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770163
StatePublished - 1 Aug 2016
Externally publishedYes
Event41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016 - Krakow, Poland
Duration: 22 Aug 201626 Aug 2016

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016

Bibliographical note

Publisher Copyright:
© Yuta Fujishige, Yuki Tsujimaru, Shunsuke Inenaga, Hideo Bannai, and Masayuki Takeda.


  • Chain simplification
  • Discrete Fréchet distance
  • Dynamic programming
  • Geometric arrangements
  • Protein structural resemblance


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