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On finding minimal absent words.

Pinho AJ, Ferreira PJ, Garcia SP, Rodrigues JM - BMC Bioinformatics (2009)

Bottom Line: The words of this new class are minimal in the sense that if their leftmost or rightmost character is removed, then the resulting word is no longer an absent word.Because the set of minimal absent words that we propose is much larger than the set of the shortest absent words, it is potentially more useful for applications that require a richer variety of absent words.Nevertheless, the number of minimal absent words is still manageable since it grows at most linearly with the string size, unlike generic absent words that grow exponentially.

View Article: PubMed Central - HTML - PubMed

Affiliation: Signal Processing Lab, DETI/IEETA, University of Aveiro, 3810-193 Aveiro, Portugal. ap@ua.pt

ABSTRACT

Background: The problem of finding the shortest absent words in DNA data has been recently addressed, and algorithms for its solution have been described. It has been noted that longer absent words might also be of interest, but the existing algorithms only provide generic absent words by trivially extending the shortest ones.

Results: We show how absent words relate to the repetitions and structure of the data, and define a new and larger class of absent words, called minimal absent words, that still captures the essential properties of the shortest absent words introduced in recent works. The words of this new class are minimal in the sense that if their leftmost or rightmost character is removed, then the resulting word is no longer an absent word. We describe an algorithm for generating minimal absent words that, in practice, runs in approximately linear time. An implementation of this algorithm is publicly available at ftp://www.ieeta.pt/~ap/maws.

Conclusion: Because the set of minimal absent words that we propose is much larger than the set of the shortest absent words, it is potentially more useful for applications that require a richer variety of absent words. Nevertheless, the number of minimal absent words is still manageable since it grows at most linearly with the string size, unlike generic absent words that grow exponentially. Both the algorithm and the concepts upon which it depends shed additional light on the structure of absent words and complement the existing studies on the topic.

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Related in: MedlinePlus

Suffix tree for string S$ = ACT AACT G$.
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Related In: Results  -  Collection

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Figure 2: Suffix tree for string S$ = ACT AACT G$.

Mentions: Figure 2 shows the suffix tree corresponding to the string of Example 1, using "$" as the terminating character.


On finding minimal absent words.

Pinho AJ, Ferreira PJ, Garcia SP, Rodrigues JM - BMC Bioinformatics (2009)

Suffix tree for string S$ = ACT AACT G$.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2698904&req=5

Figure 2: Suffix tree for string S$ = ACT AACT G$.
Mentions: Figure 2 shows the suffix tree corresponding to the string of Example 1, using "$" as the terminating character.

Bottom Line: The words of this new class are minimal in the sense that if their leftmost or rightmost character is removed, then the resulting word is no longer an absent word.Because the set of minimal absent words that we propose is much larger than the set of the shortest absent words, it is potentially more useful for applications that require a richer variety of absent words.Nevertheless, the number of minimal absent words is still manageable since it grows at most linearly with the string size, unlike generic absent words that grow exponentially.

View Article: PubMed Central - HTML - PubMed

Affiliation: Signal Processing Lab, DETI/IEETA, University of Aveiro, 3810-193 Aveiro, Portugal. ap@ua.pt

ABSTRACT

Background: The problem of finding the shortest absent words in DNA data has been recently addressed, and algorithms for its solution have been described. It has been noted that longer absent words might also be of interest, but the existing algorithms only provide generic absent words by trivially extending the shortest ones.

Results: We show how absent words relate to the repetitions and structure of the data, and define a new and larger class of absent words, called minimal absent words, that still captures the essential properties of the shortest absent words introduced in recent works. The words of this new class are minimal in the sense that if their leftmost or rightmost character is removed, then the resulting word is no longer an absent word. We describe an algorithm for generating minimal absent words that, in practice, runs in approximately linear time. An implementation of this algorithm is publicly available at ftp://www.ieeta.pt/~ap/maws.

Conclusion: Because the set of minimal absent words that we propose is much larger than the set of the shortest absent words, it is potentially more useful for applications that require a richer variety of absent words. Nevertheless, the number of minimal absent words is still manageable since it grows at most linearly with the string size, unlike generic absent words that grow exponentially. Both the algorithm and the concepts upon which it depends shed additional light on the structure of absent words and complement the existing studies on the topic.

Show MeSH
Related in: MedlinePlus