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lecture_notes:06-01-2015 [2015/06/01 13:35]
charles created
lecture_notes:06-01-2015 [2015/06/01 16:09]
jaredc
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 +===== Suffix Arrays =====
 +
 +Example Suffix Array, A[ ], of "​$banana"​
 +
 +{{:​lecture_notes:​screen_shot_2015-06-01_at_3.42.20_pm.png|}}
 +
 +===== Burrows Wheeler Transform =====
 +
 +An example BWT of "​^BANANA|"​
 +
 +{{:​lecture_notes:​screen_shot_2015-06-01_at_3.41.29_pm.png|}}
 +
 +===== FM Index =====
 +
 +An FM-index is created by first taking the Burrows-Wheeler transform (BWT) of the input text. For example, the BWT of the string T = "​abracadabra"​ is "​ard$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.
 +
 +{{:​lecture_notes:​screen_shot_2015-06-01_at_3.44.14_pm.png|}}
 +
 + 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.
 +
 +{{:​lecture_notes:​screen_shot_2015-06-01_at_3.43.25_pm.png|}}
 +
 +The function Occ(c, k) is the number of occurrences of character c in the prefix L[1..k]
 +
 +{{:​lecture_notes:​screen_shot_2015-06-01_at_3.43.33_pm.png|}}
 +
 +
 <​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]] 
 + 
 +[[http://​www.ncbi.nlm.nih.gov/​pubmed/​19451168|BWT paper]] 
  
lecture_notes/06-01-2015.txt · Last modified: 2015/06/01 16:15 by jaredc