Abstract
Given a fixed alignment scoring scheme, the bounded length (respectively, bounded total length) SmithWaterman alignment problem on a pair of strings of lengths m, n, asks for the maximum alignment score across all substring pairs, such that the first substring's length (respectively, the sum of the two substrings' lengths) is above the given threshold w. The latter problem was introduced by Arslan and Egecioglu under the name "local alignment with length threshold". They proposed a dynamic programming algorithm solving the problem in time O(mn^2), and also an approximation algorithm running in time O(rmn), where r is a parameter controlling the accuracy of approximation. We show that both these problems can be solved exactly in time O(mn), assuming a rational scoring scheme; furthermore, this solution can be used to obtain an exact algorithm for the normalised bounded total length Smith  Waterman alignment problem, running in time O(mn log n). Our algorithms rely on the techniques of fast windowsubstring alignment and implicit unitMonge matrix searching, developed previously by the author and others.
BibTeX  Entry
@InProceedings{tiskin:LIPIcs:2019:11046,
author = {Alexander Tiskin},
title = {{BoundedLength SmithWaterman Alignment}},
booktitle = {19th International Workshop on Algorithms in Bioinformatics (WABI 2019)},
pages = {16:116:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959771238},
ISSN = {18688969},
year = {2019},
volume = {143},
editor = {Katharina T. Huber and Dan Gusfield},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2019/11046},
URN = {urn:nbn:de:0030drops110461},
doi = {10.4230/LIPIcs.WABI.2019.16},
annote = {Keywords: sequence alignment, local alignment, Smith, Waterman alignment, matrix searching}
}
Keywords: 

sequence alignment, local alignment, Smith, Waterman alignment, matrix searching 
Collection: 

19th International Workshop on Algorithms in Bioinformatics (WABI 2019) 
Issue Date: 

2019 
Date of publication: 

03.09.2019 