Table 4.

MCS = Reduce($\mathcal{H}$, J, S)
1: // Argument:
2: // $\mathcal{H}$, a collection of cut sets for objective reaction
3: // set J ⊂ N in system S ∈ ℝm × n
4: // Output:
5: // MCS, a collection of MCS for J
6:
7: MCS, Done = empty collection
8: for all sets H in collection $\mathcal{H}$do
9:   ToDo = {H};
10:   while ToDo is not empty do
11:   $\overline{H}$ = a lowest cardinality set from ToDo
12:   //Apply LP based test to all
13:   //immediate subsets of $\overline{H}$ to determine
14:   //which cut at least one flux in objective set J
15:   $\mathcal{D}$ = collection of size |$\overline{H}$| - 1 subsets of $\overline{H}$ that are also cut sets for objective set J in S
16:   add $\overline{H}$ to collection Done
17:   if $\mathcal{D}$ is empty then
18:      add $\overline{H}$ to collection MCS
19:   else if $\mathcal{D}$ contains one set then
20:      add sole set in $\mathcal{D}$ to MCS and Done
21:   else
22:      add sets in $\mathcal{D}$ to ToDo
23:   end if
24:      Remove from ToDo super sets of any set in collection Done
25:   end while
26: end for
27: return MCS