### Abstract

The Local/Global Alignment (Zemla, 2003), or LGA, is a popular method for the comparison of protein structures. One of the two components of LGA requires us to compute the longest common contiguous segments between two protein structures. That is, given two structures A = (a _{1}, ..., a _{n} ) and B = (b _{1}, ..., b _{n} ) where a _{k} , b _{k} ∈ ℝ ^{3}, we are to find, among all the segments f = (a _{i} ,...,a _{j} ) and g = (b _{i} ,...,b _{j} ) that fulfill a certain criterion regarding their similarity, those of the maximum length. We consider the following criteria: (1) the root mean square deviation (RMSD) between f and g is to be within a given t ∈ ℝ; (2) f and g can be superposed such that for each k, i ≤ k ≤ j, ||a _{k} - b _{k} || ≤ t for a given t ∈ . We give an algorithm of time complexity when the first requirement applies, where is the maximum length of the segments fulfilling the criterion. We show an FPTAS which, for any ε∈ ℝ, finds a segment of length at least l, but of RMSD up to (1 + ε)t, in O(nlogn + n/ε) time. We propose an FPTAS which for any given ε∈ ℝ, finds all the segments f and g of the maximum length which can be superposed such that for each k, i ≤ k ≤ j, ||a _{k} - b _{k} || ≤ (1 + ε) t, thus fulfilling the second requirement approximately. The algorithm has a time complexity of O(nlog ^{2} n/ε ^{5}) when consecutive points in A are separated by the same distance (which is the case with protein structures).

Original language | English |
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Title of host publication | Combinatorial Pattern Matching - 23rd Annual Symposium, CPM 2012, Proceedings |

Pages | 334-348 |

Number of pages | 15 |

DOIs | |

Publication status | Published - Jul 4 2012 |

Event | 23rd Annual Symposium on Combinatorial Pattern Matching, CPM 2012 - Helsinki, Finland Duration: Jul 3 2012 → Jul 5 2012 |

### 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 | 7354 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 23rd Annual Symposium on Combinatorial Pattern Matching, CPM 2012 |
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Country | Finland |

City | Helsinki |

Period | 7/3/12 → 7/5/12 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Combinatorial Pattern Matching - 23rd Annual Symposium, CPM 2012, Proceedings*(pp. 334-348). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7354 LNCS). https://doi.org/10.1007/978-3-642-31265-6_27