Table 1 Time complexity using O-Notation

1) Semantical grouping

O(N _p (N _i  +  log N _i )

  By type

O(1)

  By property

O(N _i  + log N _i )

2) Geometric comparison

\( O\left({N}_p^2{N}^2\right) \)

  Topological comparison

O(N log N)

  Compare underlying point sets

O(N²)

  Removing scale and translation

O(N)

  Create H = Q*Q’

O(N²)

  Singular value decomposition

O(1)

  Point comparison p’ = M*p

O(N) or O(N²)

3) Share identified duplicates

O(N _p N²)

  Assign representation

O(1)

  Pre-multiply transformation

O(N²)

∑

O(N _p (N _i  log N _i  + N _p N²))