Algorithm 5.

[combinations] = GENERATE_CANDIDATES_PARALLEL (K)

Input:
	current nullspace matrix ${\text{K}}_{\text{q}\times {\text{n}}_{\text{ems}}}=\left[\begin{array}{l}{\text{R}}^{(1)}\hfill \\ {\text{R}}^{(2)}\hfill \end{array}\right]$
Output:
	pairs of indices of columns forming candidates (combinations)
1:	irrev + ⇐ {i: ${\text{R}}_{1,\text{i}}^{(2)}>0$ and (∃j: jth reaction is irreversible, ${\text{R}}_{\text{j},\text{i}}^{(1)}\ne 0$)}
2:	irrev − ⇐ {i: ${\text{R}}_{1,\text{i}}^{(2)}<0$ and (∃j: jth reaction is irreversible, ${\text{R}}_{\text{j},\text{i}}^{(1)}\ne 0$)}
3:	rev ⇐ {i: ${\text{R}}_{1,\text{i}}^{(2)}\ne 0$ and (∀j: jth reaction is reversible or ${\text{R}}_{\text{j},\text{i}}^{(1)}=0$)}
4:	irrev_p− ⇐ {i: i ∈ irrev− and i = proc_id(mod P)}
5:	rev_p ⇐ {i: i ∈ rev and i = proc_id(mod P)}
6:	S ⇐ {(ii, jj): (ii, jj) ∈ (irrev + × irrev_p−) ∪ ( (irrev+ ∪ irrev_p− ∪ rev_p) × rev)}
7:	for each (ii, jj) ∈ S do
8:	form candidate column from the pair of columns indexed by (ii, jj)
9:	if candidate satisfies Proposition 4 add to combinations
10:	end for