Inversion of a part of the numerator relationship matrix using pedigree information

Table 7 Estimated computational complexity ¹ of Algorithm B

Procedure	Complexity for line i	Proportion	Complexity on n lines
EMPTY	1	p _E	p_E · O(n)
LS	O(k³) + O(k²) + O(k)	p _L	p_P · [O(n · k³) + O(n · k²) + O(n · k)]
PROD	O(k²) + O(k · i)	p _P	p_P · [O(n · k²) + O(n² · k)]
Total	$\begin{array}{l} O (k^{3}) + O (k^{2}) \\ + O (k \cdot i) + O (k) \end{array}$	1	$\begin{array}{l} p_{P} \cdot O (n^{2} \cdot k) + p_{L} \cdot O (n \cdot k^{3}) + (p_{L} + p_{P}) \cdot O (n \cdot k^{2}) \\ + p_{L} \cdot O (n \cdot k) + p_{E} \cdot O (n) \end{array}$

Matrix is of order n and average number of contributors is k;
¹computational complexity is assessed as the expected number of floating-point multiplications to be performed.

ISSN: 1297-9686