Algorithm 4.

[K]=PARALLEL_NSP(N, K)

Input:
	reduced stoichiometry matrix (Nm×q); initial nullspace matrix ${\text{K}}_{\text{q}\times (\text{q}-\text{m})}=\left[\begin{array}{l}{\text{R}}^{(1)}\hfill \\ {\text{R}}^{(2)}\hfill \end{array}\right]$
Output:
	bit-valued matrix of elementary modes Kq×nems
1:	for k = q − m + 1 to q do
2:	combinations ⇐ GENERATE_CANDIDATES_PARALLEL (K)
3:	combinations ⇐ RADIXSORT(R(1), combinations, width)
4:	combinations ⇐ REMOVE_DUPLICATES(R(1), combinations)
5:	combinations ⇐ RANKTESTS (N, R(1), combinations)
6:	{communicate columns and merge}
7:	combinations ⇐ COMMUNICATE_TREE(R(1), combinations)
8:	K ⇐ EXPAND(K, combinations)
9:	end for