Table 3 Employing an algorithm for the LCP problem to solve the MAD problem

Input:

sequences P = (p₁,…,p _n ), Q = (q₁,…,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 $u-l\le \frac{\sqrt{12c_{\mathit{\text{max}}}^2}-\sqrt{12c_{\mathit{\text{max}}}^2-1}}{\sqrt{2\ell }}$,

Output the most recent LCP solution of size no less than ℓ.

Otherwise, repeat Steps 2-5.