Dynamic Programing
Dynamic Programing Dynamic Programing
Needleman-Wunsch Algorithm (Cont.) A dynamic programming algorithm for optimal global alignment Given: Two sequences V = (v1v2...vn) and W =(w1w2...wm). (|V| = n and |W|= m) Goal: Find the best scoring alignment in which all residues of both sequences are included. The score is usually a measure of similarity. Requirement: - A matrix NW of optimal scores of subsequence alignments. NW has size (n+1)x(m+1). - Score matrix - Defined gap penalty
Needleman-Wunsch Algorithm (Cont.) Calculation Let NW(i,j) be the optimal alignment score of aligning V[1...i] and W[1...j] 0 w1 ... wj ... wm v1 : (I) +s(vi, wj) (III) +gap vi (II) +gap : vn Optimal alignment score
- Page 1 and 2: Dynamic Programming and Pairwise Se
- Page 3 and 4: Importance of Sequence Alignment
- Page 5 and 6: Alignment Operation Transforming on
- Page 7 and 8: Difficulties in measuring sequence
- Page 9 and 10: Efficient way to find a best alignm
- Page 11 and 12: Problems Solvable by Dynamic Progra
- Page 13: Property of DP problems • Have ov
- Page 16 and 17: I. Global Alignment Classes of Pair
- Page 18 and 19: Classes of Pairwise Alignment: I. G
- Page 20 and 21: Classes of Pairwise Alignment: I. G
- Page 22 and 23: Global Alignment spans all the resi
- Page 24 and 25: Scoring matrix represents a specifi
- Page 28 and 29: Needleman-Wunsch Algorithm (Cont.)
- Page 30 and 31: Needleman-Wunsch Algorithm (Cont.)
- Page 32 and 33: Needleman-Wunsch Algorithm Efficien
- Page 34 and 35: Needleman-Wunsch Algorithm for any
- Page 36 and 37: Needleman-Wunsch Algorithm for any
- Page 38 and 39: Local Alignment finds the most simi
- Page 40 and 41: Smith-Waterman Algorithm (Cont.)
- Page 42 and 43: Smith-Waterman Algorithm (Cont.) v1
- Page 44 and 45: Smith-Waterman Algorithm (Cont.) Ex
- Page 46 and 47: Which alignment to use Example 1. O
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- Page 54 and 55: Which alignment to use (Cont.) Exam
- Page 56 and 57: Versatility of DP Algorithm • Mem
- Page 58 and 59: References - Gusfield D. Algorithms
Needleman-Wunsch Algorithm (Cont.)<br />
Calculation<br />
Let NW(i,j) be the optimal alignment score of aligning V[1...i] and W[1...j]<br />
0<br />
w1 ... wj ... wm<br />
v1<br />
:<br />
(I)<br />
+s(vi, wj)<br />
(III)<br />
+gap<br />
vi<br />
(II)<br />
+gap<br />
:<br />
vn<br />
Optimal<br />
alignment<br />
score
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