## Bernoulli

• Bernoulli
• Volume 20, Number 3 (2014), 1292-1343.

### Optimal alignments of longest common subsequences and their path properties

#### Abstract

We investigate the behavior of optimal alignment paths for homologous (related) and independent random sequences. An alignment between two finite sequences is optimal if it corresponds to the longest common subsequence (LCS). We prove the existence of lowest and highest optimal alignments and study their differences. High differences between the extremal alignments imply the high variety of all optimal alignments. We present several simulations indicating that the homologous (having the same common ancestor) sequences have typically the distance between the extremal alignments of much smaller size than independent sequences. In particular, the simulations suggest that for the homologous sequences, the growth of the distance between the extremal alignments is logarithmical. The main theoretical results of the paper prove that (under some assumptions) this is the case, indeed. The paper suggests that the properties of the optimal alignment paths characterize the relatedness of the sequences.

#### Article information

Source
Bernoulli, Volume 20, Number 3 (2014), 1292-1343.

Dates
First available in Project Euclid: 11 June 2014

https://projecteuclid.org/euclid.bj/1402488941

Digital Object Identifier
doi:10.3150/13-BEJ522

Mathematical Reviews number (MathSciNet)
MR3217445

Zentralblatt MATH identifier
1312.60004

#### Citation

Lember, Jüri; Matzinger, Heinrich; Vollmer, Anna. Optimal alignments of longest common subsequences and their path properties. Bernoulli 20 (2014), no. 3, 1292--1343. doi:10.3150/13-BEJ522. https://projecteuclid.org/euclid.bj/1402488941

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