From: The difficulty of protein structure alignment under the RMSD
Input: | sequences P = (p_{1},…,p_{ n }), Q = (q_{1},…,q_{ m }) and $\ell \in \mathbb{I}$. |
Without loss of generality assume m ≥ n. | |
Output: | (i) subsequences P^{′} ⊆ P, Q^{′} ⊆ Q, |P^{′}| = |Q^{′}|, and |
(ii) mapping f:P^{′} ↦ Q^{′}, fulfilling the following conditions: | |
(A) |P^{′}| = ℓ, | |
(B) d = RMSD(P^{′},f(p^{′})) is minimized. | |
1. | l ← 0, u ← ℓ c_{ max } |
2. | m ← 1/2(l + u) |
3. | Call LCP to solve the instance (P,Q,m). |
4. | If the LCP solution has size no less than ℓ |
u ← m | |
else | |
l ← m | |
5. | If $u-l\le \frac{\sqrt{12{c}_{\mathit{\text{max}}}^{2}}-\sqrt{12{c}_{\mathit{\text{max}}}^{2}-1}}{\sqrt{2\ell}}$, |
Output the most recent LCP solution of size no less than ℓ. | |
Otherwise, repeat Steps 2-5. |