MSA-Lecture12

MSA-Lecture12 - Rapid Global Alignments How to align...

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Rapid Global Alignments How to align genomic sequences in (more or less) linear time
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Methods to CHAIN Local Alignments Sparse Dynamic Programming O(N log N)
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The Problem: Find a Chain of Local Alignments (x,y) (x’,y’) requires x < x’ y < y’ Each local alignment has a weight FIND the chain with highest total weight
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Sparse DP for rectangle chaining 1,…, N: rectangles (h j , l j ): y-coordinates of rectangle j w(j): weight of rectangle j V(j): optimal score of chain ending in j L: list of triplets (l j , V(j), j) L is sorted by l j L is implemented as a balanced binary tree y h l
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Sparse DP for rectangle chaining Main idea: Sweep through x- coordinates To the right of b , anything chainable to a is chainable to b Therefore, if V(b) > V(a) , rectangle a is “useless” – remove it In L, keep rectangles j sorted with increasing l j - coordinates sorted with increasing V(j) V(b) V(a)
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Sparse DP for rectangle chaining Go through rectangle x-coordinates, from left to right: 1. When on the leftmost end of rectangle i, compute V(i) a. j: rectangle in L, with largest l j < h i b. V(i) = w(i) + V(j) 2. When on the rightmost end of i, possibly store V(i) in L: a. j: rectangle in L, with largest l j l i b. If V(i) > V(j): i. INSERT (l i , V(i), i) in L ii. REMOVE all (l k , V(k), k) with V(k) k l i i j
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Example x y 1: 5 3: 3 2: 6 4: 4 5: 2 2 5 6 9 10 11 12 14 15 16
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Time Analysis 1. Sorting the x-coords takes O(N log N) 2. Going through x-coords: N steps 3. Each of N steps requires O(log N) time: Searching L takes log N Inserting to L takes log N All deletions are consecutive, so log N per deletion Each element is deleted at most once: N log N for all deletions Recall that INSERT, DELETE, SUCCESSOR, take O(log N) time in a balanced binary search tree
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Fast Global Alignment Algorithms 1. FIND local alignments 2. CHAIN local alignments FIND
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This note was uploaded on 02/13/2012 for the course CS 91.510 taught by Professor Staff during the Fall '09 term at UMass Lowell.

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MSA-Lecture12 - Rapid Global Alignments How to align...

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