Paper Info
Title
Optimal Computation of Avoided Words.
Abstract
The deviation of the observed frequency of a word w from its expected frequency in a given sequence x is used to determine whether or not the word is avoided. This concept is particularly useful in DNA linguistic analysis. The value of the standard deviation of w, denoted by std(w), effectively characterises the extent of a word by its edge contrast in the context in which it occurs. A word w of length k > 2 is a rho-avoided word in x if std(w) <= rho, for a given threshold rho < 0. Notice that such a word may be completely absent from x. Hence computing all such words naively can be a very time-consuming procedure, in particular for large k. In this article, we propose an O(n)-time and O(n)-space algorithm to compute all rho-avoided words of length k in a given sequence x of length n over a fixed-sized alphabet. We also present a time-optimal O(sigma n)-time algorithm to compute all rho-avoided words (of any length) in a sequence of length n over an integer alphabet of size sigma. We provide a tight asymptotic upper bound for the number of rho-avoided words over an integer alphabet and the expected length of the longest one. We make available an implementation of our algorithm. Experimental results, using both real and synthetic data, show the efficiency of our implementation.
Year
DOI
Venue
2016
10.1007/978-3-319-43681-4_1
ALGORITHMS IN BIOINFORMATICS
DocType
Volume
ISSN
Journal
9838
0302-9743
Citations 
PageRank 
References 
1
0.40
4
Authors
7
Name
Order
Citations
PageRank
Yannis Almirantis1786.84
Panagiotis Charalampopoulos2299.41
Jia Gao3112.26
Costas S. Iliopoulos41534167.43
Manal Mohamed510212.62
Solon P. Pissis628157.09
Dimitris Polychronopoulos7765.12