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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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Example of the growth of the number of generic absent words and minimal absent words as a function of word size, n. Plots of the number of generic absent words and minimal absent words for the case of the M. genitalium organism. It can be seen that the number of minimal absent words grows until a maximum and then decreases towards zero. On the contrary, the number of generic absent words grows exponentially. For comparison, we also included the graphic of the function 4n. This behavior has also been observed in the other sequences.
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Figure 7: Example of the growth of the number of generic absent words and minimal absent words as a function of word size, n. Plots of the number of generic absent words and minimal absent words for the case of the M. genitalium organism. It can be seen that the number of minimal absent words grows until a maximum and then decreases towards zero. On the contrary, the number of generic absent words grows exponentially. For comparison, we also included the graphic of the function 4n. This behavior has also been observed in the other sequences.

Mentions: Figure 7 shows how the number of generic absent words and minimal absent words grow as a function of the length of the word, n. As can be observed, the number of minimal absent words grows until a maximum value and then decreases beyond that point. In opposition, the number of generic absent words grows exponentially. This is confirmed by the 4n curve also plotted in Fig. 7.


On finding minimal absent words.

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

Example of the growth of the number of generic absent words and minimal absent words as a function of word size, n. Plots of the number of generic absent words and minimal absent words for the case of the M. genitalium organism. It can be seen that the number of minimal absent words grows until a maximum and then decreases towards zero. On the contrary, the number of generic absent words grows exponentially. For comparison, we also included the graphic of the function 4n. This behavior has also been observed in the other sequences.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 7: Example of the growth of the number of generic absent words and minimal absent words as a function of word size, n. Plots of the number of generic absent words and minimal absent words for the case of the M. genitalium organism. It can be seen that the number of minimal absent words grows until a maximum and then decreases towards zero. On the contrary, the number of generic absent words grows exponentially. For comparison, we also included the graphic of the function 4n. This behavior has also been observed in the other sequences.
Mentions: Figure 7 shows how the number of generic absent words and minimal absent words grow as a function of the length of the word, n. As can be observed, the number of minimal absent words grows until a maximum value and then decreases beyond that point. In opposition, the number of generic absent words grows exponentially. This is confirmed by the 4n curve also plotted in Fig. 7.

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