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Table 4 A polynomial time algorithm for the MAD problem

From: The difficulty of protein structure alignment under the RMSD

Input: sequences P = (p1,…,p n ), Q = (q1,…,q m ) and I.
  Without loss of generality assume m ≥ n.
Output: (i) subsets PP, QQ, |P| = |Q|, and
  (ii) mapping f:P ′ Q, fulfilling the following conditions:
  (A) |P| = ,
  (B) d = RMSD(P,f(p)) is minimized.
1. For each translation t {I/| -  c max  ≤ I ≤  c max }3,
  For each 3 × 3 matrix M, where eM, e {I/2|-,
  {4 3 c max 2 I4 3 c max 2 }
  Compute rotation matrix R from M.
  QRQ-t.
  Apply an algorithm for the case where the superposition
  is known to P and Q (as discussed in the ‘Complexity Of
  The LCP And MAD When The Optimal Superposition Is
  Known’ section), and denote the solution MAD(P, Q).
2. Output the MAD(P, Q) of the smallest RMSD as the solution.