1. Space-Saving Strategies for Analyzing Biomolecular Sequences
Kun-Mao Chao (趙坤茂)
Department of Computer Science and Information Engineering
National Taiwan University, Taiwan
URL:

2. Linear-space ideas Hirschberg, 1975; Myers and Miller, 1988
Partition line
m/2

3. Consider the case where the penalty for a gap is merely proportional to the gap’s length, i.e., k x β for a k-symbol gap.

8. Two subproblems ½ original problem size

9. Four subproblems ¼ original problem size

10. Time and Space Complexity
Space: O(m+n)
Time: O(mn)*(1+ ½ + ¼ + …) = O(mn) 2

11. Band Alignment (Joint work with W. Pearson and W. Miller)
Sequence A
Sequence B

12. Band Alignment in Linear Space
The remaining subproblems are no longer only half of the original problem. In worst case, this could cause an additional log n factor in time.
O(log n)
O(nW)*(1+1+…+1)
=O(nW log n)

13. Band Alignment in Linear Space

14. Parallelogram

15. Parallelogram

16. Yet another partition line
Band width W

17. Yet another partition line

18. Arbitrary region

19. Arbitrary region