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lecture_notes:06-01-2015 [2015/06/01 20:35] charles created |
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+ | ===== Suffix Arrays ===== | ||
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+ | Example Suffix Array, A[ ], of "$banana" | ||
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+ | {{:lecture_notes:screen_shot_2015-06-01_at_3.42.20_pm.png|}} | ||
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+ | ===== Burrows Wheeler Transform ===== | ||
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+ | An example BWT of "^BANANA|" | ||
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+ | {{:lecture_notes:screen_shot_2015-06-01_at_3.41.29_pm.png|}} | ||
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+ | ===== FM Index ===== | ||
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+ | An FM-index is created by first taking the Burrows-Wheeler transform (BWT) of the input text. For example, the BWT of the string T = "abracadabra" is "ard$rcaaaabb", and here it is represented by the matrix M where each row is a rotation of the text that has been sorted. The transform corresponds to the last column labeled L. | ||
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+ | {{:lecture_notes:screen_shot_2015-06-01_at_3.44.14_pm.png|}} | ||
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+ | C[c] is a table that, for each character c in the alphabet, contains the number of occurrences of lexically smaller characters in the text. | ||
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+ | {{:lecture_notes:screen_shot_2015-06-01_at_3.43.25_pm.png|}} | ||
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+ | The function Occ(c, k) is the number of occurrences of character c in the prefix L[1..k] | ||
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+ | {{:lecture_notes:screen_shot_2015-06-01_at_3.43.33_pm.png|}} | ||
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+ | The program [[http://bowtie-bio.sourceforge.net/index.shtml|Bowtie]] uses an FM index technique | ||
+ | * [[http://www.genomebiology.com/2009/10/3/R25|Ultrafast and memory-efficient alignment of short DNA sequences to the human genome]] | ||
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<code> | <code> | ||
Charles M. - BWT Notes | Charles M. - BWT Notes | ||
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Additional resources and better examples can be found below: | Additional resources and better examples can be found below: | ||
- | {{BWT and FM Index tutorial:http://www.cs.jhu.edu/~langmea/resources/bwt_fm.pdf}} | ||
+ | [[http://www.cs.jhu.edu/~langmea/resources/bwt_fm.pdf|BWT and FM Index tutorial]] | ||
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+ | [[http://www.ncbi.nlm.nih.gov/pubmed/19451168|BWT paper]] |