## Abstract

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, Aʹ and Bʹ, is of length at most k and the discrete Fréchet distance between Aʹ and Bʹ is at most δ, where k and δ 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^{2}n^{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.

Original language | English |
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Title of host publication | Algorithms and Data Structures - 14th International Symposium, WADS 2015, Proceedings |

Editors | Frank Dehne, Jorg-Rudiger Sack, Ulrike Stege |

Publisher | Springer Verlag |

Pages | 351-362 |

Number of pages | 12 |

ISBN (Print) | 9783319218397 |

DOIs | |

State | Published - 2015 |

Externally published | Yes |

Event | 14th International Symposium on Algorithms and Data Structures, WADS 2015 - Victoria, Canada Duration: 5 Aug 2015 → 7 Aug 2015 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 9214 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 14th International Symposium on Algorithms and Data Structures, WADS 2015 |
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Country/Territory | Canada |

City | Victoria |

Period | 5/08/15 → 7/08/15 |

### Bibliographical note

Publisher Copyright:© Springer International Publishing Switzerland 2015.