Algorithm 2 Sequence Reconstruction
Input:
	Sequence S; CS-tree CT constructed based on candidate k-sequences Ck;
	Maximal Length Constraint lmax;
Output:
	Sequence Ŝ;
1:	subCT ← build_CSTree (CT, S);
2:	for each candidate sequence cs in S do
3:	cs.GN ← find_GNodes (cs, subCT);
4:	cs.score ← sum_childNodes (cs.GN);
5:	end for
6:	s ← Select a candidate sequence;
7:	insert (Ŝ, s); update_tree(subCT, s);
8:	while |Ŝ| < lmax do
9:	GN ← find_GNodes (Ŝ, subCT);
10:	if GN.childNodeNum() ≠ 0 then
11:	for each g-node gn in GN do
12:	Item_GNode_Map ← map_item_g-node (gn);
13:	end for
14:	item i ← find_item (Item_GNode_Map);
15:	insert (Ŝ, i); update_Tree (subCT, i, Item_GNode_Map);
16:	else
17:	for each c-node cn in subCT do
18:	cs ← cn's associated sequence;
19:	cs.GN ← find_GNodes (cs, subCT);
20:	cs.score ← sum_childNodes (cs.GN);
21:	end for
22:	s ← Select a candidate sequence;
23:	insert (Ŝ, s); update_Tree(subCT, s);
24:	end if
25:	end while
26:	return Ŝ;