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Space-Saving Strategies for Computing Δ-points

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Presentation on theme: "Space-Saving Strategies for Computing Δ-points"— Presentation transcript:

1 Space-Saving Strategies for Computing Δ-points
Kun-Mao Chao (趙坤茂) Department of Computer Science and Information Engineering National Taiwan University, Taiwan WWW:

2 Δ-points S-(i, j): the best score of a path from (0, 0) to (i, j).
S+(i, j): the best score of a path from (i, j) to (M, N). Δ-points: S-(i, j) + S+( i, j) >= Δ S - S +

3 The leftmost/rightmost Δ-paths
For simple scoring schemes, finding the leftmost Δ-path and the rightmost Δ-path is easy. For affine gap penalties, it is more complicated.

4 Two alignments may not intersect!

5 Method 1: O(MN) time; O(MN) space

6 Method 2: O(M2N) time; O(N) space
Each row takes O(MN) time. In total, O(M) x O(MN) = O(M2N) S + M

7 Method 3: O(MN) time; O(N) space

8 Method 4: O(MN log M) time; O(N log M) space

9 Method 4: O(MN log M) time; O(N log M) space (cont’d)
O(log M) layers M O(N) O(N) O(N) O(N) O(N)

10 Method 5: O(MN log min {M, N}) time; O(M+N) space

11 Method 6: O(MN log log min {M, N}) time; O(M+N) space
Real Size 1/25 1/23 N 1/210 1/25 1/22 M 1/29 1/219

12 Method 7: O(1/ε MN) time; O(1/ε MεN) space Here we use ε= 1/2 to illustrate the idea.
Solve each M1/2N problem M1/2 S - S + M

13 Method 8: O(1/εMN) time; O(1/ε M1+ε+ N) space Here we use ε= 1/2 to illustrate the idea.
O(N) M Solve each M1/2M problem M1/2 S - S + M

14 Methods Method 1: O(MN) time; O(MN) space
Method 2: O(M2N) time; O(M) space Method 3: O(MN) time; O(M) space Method 4: O(MN log M) time; O(N log M) space Method 5: O(MN log min {M, N}) time; O(M+N) space Method 6: O(MN log log min {M, N}) time; O(M+N) space Method 7: O(1/εMN) time; O(1/ ε MεN) space Method 8: O(1/εMN) time; O(1/ε M1+ε+ N) space

15 Bonus points O(MN) time; O(M+N) space
o(MN log log min {M, N}) time; O(M+N) space O(1/εMN) time; o(1/ε M1+ε+N) space


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