2016/04/29 by Yannis Almirantis, Almirantis, Yannis, Panagiotis Charalampopoulos +11
Biochemistry, Genetics and Molecular Biology · Computer Science · #Algorithms and Data Compression #DNA and Biological Computing #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1604.08760
openalex publication_date 2016/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ρ-avoided word in x if std(w) ≤ ρ, for a given threshold ρ< 0. Notice that such a word may be completely absent from x. Hence computing all such words na"ıvely 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 ρ-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(σn)-time and O(σn)-space algorithm to compute all ρ-avoided words (of any length) in a sequence of length n over an alphabet of size σ. Furthermore, we provide a tight asymptotic upper bound for the number of ρ-avoided words and the expected length of the longest one. We make available an open-source implementation of our algorithm. Experimental results, using both real and synthetic data, show the efficiency of our implementation.