Optimal Computation of Avoided Words

Yannis Almirantis; Panagiotis Charalampopoulos; Jia Gao; Costas S. Iliopoulos; Manal Mohamed; Solon P. Pissis; Dimitris Polychronopoulos

doi:10.1007/978-3-319-43681-4_1

Optimal Computation of Avoided Words

Yannis Almirantis, Panagiotis Charalampopoulos, Jia Gao, Costas S. Iliopoulos, Manal Mohamed, Solon P. Pissis, Dimitris Polychronopoulos

Research output: Chapter in Book/Report/Conference proceeding › Other chapter contribution › peer-review

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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 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 naïvely 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 algorithm to compute all ρ-avoided words (of any length) in a sequence of length n over an integer alphabet of size σ. We provide a tight asymptotic upper bound for the number of ρ-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.

Original language	English
Title of host publication	Algorithms in Bioinformatics
Subtitle of host publication	16th International Workshop, WABI 2016, Aarhus, Denmark, August 22-24, 2016. Proceedings
Editors	Martin Frith, Nørgaard Christian Storm Pedersen
Publisher	Springer International Publishing Switzerland
Pages	1-13
Number of pages	13
ISBN (Electronic)	978-3-319-43681-4
ISBN (Print)	978-3-319-43680-7
DOIs	https://doi.org/10.1007/978-3-319-43681-4_1
Publication status	Published - 6 Aug 2016

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer
Volume	9838
ISSN (Print)	0302-9743

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10.1007/978-3-319-43681-4_1

Optimal Computation of Avoided_ALMIRANTIS_Firstonline6August2016_GREEN AAMAccepted author manuscript, 192 KBLicence: CC BY-NC-SA

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Almirantis, Y., Charalampopoulos, P., Gao, J., Iliopoulos, C. S., Mohamed, M., Pissis, S. P., & Polychronopoulos, D. (2016). Optimal Computation of Avoided Words. In M. Frith, & N. C. Storm Pedersen (Eds.), Algorithms in Bioinformatics: 16th International Workshop, WABI 2016, Aarhus, Denmark, August 22-24, 2016. Proceedings (pp. 1-13). (Lecture Notes in Computer Science; Vol. 9838). Springer International Publishing Switzerland. https://doi.org/10.1007/978-3-319-43681-4_1

Almirantis, Yannis ; Charalampopoulos, Panagiotis ; Gao, Jia et al. / Optimal Computation of Avoided Words. Algorithms in Bioinformatics: 16th International Workshop, WABI 2016, Aarhus, Denmark, August 22-24, 2016. Proceedings. editor / Martin Frith ; Nørgaard Christian Storm Pedersen. Springer International Publishing Switzerland, 2016. pp. 1-13 (Lecture Notes in Computer Science).

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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 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{\"i}vely 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 algorithm to compute all ρ-avoided words (of any length) in a sequence of length n over an integer alphabet of size σ. We provide a tight asymptotic upper bound for the number of ρ-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.",

author = "Yannis Almirantis and Panagiotis Charalampopoulos and Jia Gao and Iliopoulos, {Costas S.} and Manal Mohamed and Pissis, {Solon P.} and Dimitris Polychronopoulos",

year = "2016",

month = aug,

day = "6",

doi = "10.1007/978-3-319-43681-4_1",

language = "English",

isbn = "978-3-319-43680-7",

series = "Lecture Notes in Computer Science",

publisher = "Springer International Publishing Switzerland",

pages = "1--13",

editor = "Martin Frith and {Storm Pedersen}, {N{\o}rgaard Christian}",

booktitle = "Algorithms in Bioinformatics",

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Almirantis, Y, Charalampopoulos, P , Gao, J , Iliopoulos, CS , Mohamed, M , Pissis, SP & Polychronopoulos, D 2016, Optimal Computation of Avoided Words. in M Frith & NC Storm Pedersen (eds), Algorithms in Bioinformatics: 16th International Workshop, WABI 2016, Aarhus, Denmark, August 22-24, 2016. Proceedings. Lecture Notes in Computer Science, vol. 9838, Springer International Publishing Switzerland, pp. 1-13. https://doi.org/10.1007/978-3-319-43681-4_1

Optimal Computation of Avoided Words. / Almirantis, Yannis; Charalampopoulos, Panagiotis ; Gao, Jia et al.
Algorithms in Bioinformatics: 16th International Workshop, WABI 2016, Aarhus, Denmark, August 22-24, 2016. Proceedings. ed. / Martin Frith; Nørgaard Christian Storm Pedersen. Springer International Publishing Switzerland, 2016. p. 1-13 (Lecture Notes in Computer Science; Vol. 9838).

Research output: Chapter in Book/Report/Conference proceeding › Other chapter contribution › peer-review

TY - CHAP

T1 - Optimal Computation of Avoided Words

AU - Almirantis, Yannis

AU - Charalampopoulos, Panagiotis

AU - Gao, Jia

AU - Iliopoulos, Costas S.

AU - Mohamed, Manal

AU - Pissis, Solon P.

AU - Polychronopoulos, Dimitris

PY - 2016/8/6

Y1 - 2016/8/6

N2 - 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 naïvely 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 algorithm to compute all ρ-avoided words (of any length) in a sequence of length n over an integer alphabet of size σ. We provide a tight asymptotic upper bound for the number of ρ-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.

AB - 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 naïvely 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 algorithm to compute all ρ-avoided words (of any length) in a sequence of length n over an integer alphabet of size σ. We provide a tight asymptotic upper bound for the number of ρ-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.

U2 - 10.1007/978-3-319-43681-4_1

DO - 10.1007/978-3-319-43681-4_1

M3 - Other chapter contribution

SN - 978-3-319-43680-7

T3 - Lecture Notes in Computer Science

SP - 1

EP - 13

BT - Algorithms in Bioinformatics

A2 - Frith, Martin

A2 - Storm Pedersen, Nørgaard Christian

PB - Springer International Publishing Switzerland

ER -

Almirantis Y, Charalampopoulos P , Gao J , Iliopoulos CS , Mohamed M , Pissis SP et al. Optimal Computation of Avoided Words. In Frith M, Storm Pedersen NC, editors, Algorithms in Bioinformatics: 16th International Workshop, WABI 2016, Aarhus, Denmark, August 22-24, 2016. Proceedings. Springer International Publishing Switzerland. 2016. p. 1-13. (Lecture Notes in Computer Science). doi: 10.1007/978-3-319-43681-4_1

Optimal Computation of Avoided Words

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