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Table 1 Time complexity using O-Notation

From: Removing duplicated geometries in IFC models using rigid body transformation estimation and flyweight design pattern

Subroutine Complexity
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))