On the Chain Pair Simplification Problem

  • Chenglin Fan
  • Omrit Filtser
  • Matthew J. Katz
  • Tim Wylie
  • Binhai ZhuEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9214)


The problem of efficiently computing and visualizing the structural resemblance between a pair of protein backbones in 3D has led Bereg et al. [4] to pose the Chain Pair Simplification problem (CPS). In this problem, given two polygonal chains A and B of lengths m and n, respectively, one needs to simplify them simultaneously, such that each of the resulting simplified chains, \(A'\) and \(B'\), is of length at most k and the discrete Fréchet distance between \(A'\) and \(B'\) is at most \(\delta \), where k and \(\delta \) are given parameters. In this paper we study the complexity of CPS under the discrete Fréchet distance (CPS-3F), i.e., where the quality of the simplifications is also measured by the discrete Fréchet distance. Since CPS-3F was posed in 2008, its complexity has remained open. In this paper, we prove that CPS-3F is actually polynomially solvable, by presenting an \(O(m^2n^2\min \{m,n\})\) time algorithm for the corresponding minimization problem. On the other hand, we prove that if the vertices of the chains have integral weights then the problem is weakly NP-complete.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Chenglin Fan
    • 1
  • Omrit Filtser
    • 2
  • Matthew J. Katz
    • 2
  • Tim Wylie
    • 3
  • Binhai Zhu
    • 1
    Email author
  1. 1.Montana State UniversityBozemanUSA
  2. 2.Ben-Gurion University of the NegevBeer-ShevaIsrael
  3. 3.The University of Texas-Pan AmericanEdinburgUSA

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