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: http://www.csie.ntu.edu.tw/~kmchao

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

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.

Two subproblems ½ original problem size

Four subproblems ¼ original problem size

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

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

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)

Band Alignment in Linear Space

Parallelogram

Parallelogram

Yet another partition line Band width W

Yet another partition line

Arbitrary region

Arbitrary region