Translator Disclaimer
August 2014 Optimal alignments of longest common subsequences and their path properties
Jüri Lember, Heinrich Matzinger, Anna Vollmer
Bernoulli 20(3): 1292-1343 (August 2014). DOI: 10.3150/13-BEJ522


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.


Download Citation

Jüri Lember. Heinrich Matzinger. Anna Vollmer. "Optimal alignments of longest common subsequences and their path properties." Bernoulli 20 (3) 1292 - 1343, August 2014.


Published: August 2014
First available in Project Euclid: 11 June 2014

zbMATH: 1312.60004
MathSciNet: MR3217445
Digital Object Identifier: 10.3150/13-BEJ522

Rights: Copyright © 2014 Bernoulli Society for Mathematical Statistics and Probability


Vol.20 • No. 3 • August 2014
Back to Top