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lecture_notes:04-22-2011 [2011/06/08 10:29]
eyliaw [Suffix array]
lecture_notes:04-22-2011 [2015/08/09 16:06] (current)
212.129.31.47 ↷ Links adapted because of a move operation
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 ====== Burrows Wheeler Aligner ====== ====== Burrows Wheeler Aligner ======
-We discussed the [[bioinformatic_tools:​bwa]]. ​ It uses the Burrows Wheeler Transform to represent a prefix trie, allowing for short read alignment with mismatches and gaps.+We discussed the [[archive:bioinformatic_tools:​bwa]]. ​ It uses the Burrows Wheeler Transform to represent a prefix trie, allowing for short read alignment with mismatches and gaps.
  
 ===== The prefix trie ====== ===== The prefix trie ======
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    6 $GOOGOL    6 $GOOGOL
 Sort: Sort:
-   6 $GOOGO**L** +   6 $GOOGOL 
-   3 GOL$GO**O** +   3 GOL$GOO 
-   0 GOOGOL**$** +   0 GOOGOL$ 
-   5 L$GOOG**O** +   5 L$GOOGO 
-   2 OGOL$G**O** +   2 OGOL$GO 
-   4 OL$GOO**G** +   4 OL$GOOG 
-   1 OOGOL$**G**+   1 OOGOL$G
  
    S(i) = [6,​3,​0,​5,​2,​4,​1]    S(i) = [6,​3,​0,​5,​2,​4,​1]
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 C_X(a) is the number of characters lexicographically before a in X. C_X(a) is the number of characters lexicographically before a in X.
-   0 +   
-   G 1 +   ​L ​2 
-   ​L ​3 +   ​O ​3
-   ​O ​4+
 O_X(a,i) is the number of occurrences of a in B_X[0,i]. O_X(a,i) is the number of occurrences of a in B_X[0,i].
 +^ i ^ B_X[0,i] ^ O_X(G,i) ^ O_X(L,i) ^ O_X(O,i) ^
 +| 1 | L        | 0        | 1        | 0        | 
 +| 2 | LO       | 0        | 1        | 1        | 
 +| 3 | LO$      | 0        | 1        | 1        | 
 +| 4 | LO$O     | 0        | 1        | 2        | 
 +| 5 | LO$OO    | 0        | 1        | 3        | 
 +| 6 | LO$OOG ​  | 1        | 1        | 3        | 
 +| 7 | LO$OOGG ​ | 2        | 1        | 3        | 
 +
 +There are then two recursive formulas to find the start and end positions of a substring.
 +   End R_(aW) = C(a) + O(a,R_(W) - 1) + 1 or 1 if W is the empty string
 +   Start R-(aW) = C(a) + O(a,R-(W)) or (n - 1) if W is the empty string
 +Where a is the first character and W is the word.
lecture_notes/04-22-2011.1307554142.txt.gz · Last modified: 2011/06/08 10:29 by eyliaw