Algorithm 6.

[combinations] = COMMUNICATE_TREE (K, combinations)

Input:
	current nullspace matrix ${\text{K}}_{\text{q}\times {\text{n}}_{\text{ems}}}=\left[\begin{array}{l}{\text{R}}^{(1)}\hfill \\ {\text{R}}^{(2)}\hfill \end{array}\right]$;
	local set of pairs of column indices which generate new candidates (combinations)
Output:
	merged set of column-generating pairs of indices (combinations)
1:	proc_id ⇐ identifier of the local compute-node
2:	for i = 1 to log P do
3:	if proc_id = 0 (mod2i) then
4:	receive columns from compute-node proc_id + 2i−1
5:	merge the local set of columns with the received columns
6:	else
7:	send columns to compute-node proc_id − 2i−1
8:	end if
9:	end for
10:	if proc_id = 0 then
11:	broadcast the columns to all other compute-nodes
12:	end if