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function bel = tree_protocol(engine, evidence, pot_type, local_kernel, msg)
bnet = bnet_from_engine(engine);
ns = bnet.node_sizes;
onodes = find(~isemptycell(evidence));
ndoms = length(engine.gdl.doms);
prod_of_msg = cell(1, ndoms);
bel = cell(1, ndoms);
% collect to root (node to parents)
for n=engine.postorder
% absorb msgs from children
prod_of_msg{n} = mk_initial_pot(pot_type, engine.gdl.doms{n}, ns, bnet.cnodes, onodes);
for c=children(engine.tree, n)
prod_of_msg{n} = multiply_by_pot(prod_of_msg{n}, msg{c,n});
end
% send msg to parents
for p=parents(engine.tree, n)
if iter==1
temp = prod_of_msg{n};
else
temp = divide_by_pot(prod_of_msg{n}, old_msg{p,n});
end
temp = multiply_by_pot(temp, local_kernel{n});
temp2 = marginalize_pot(temp, engine.gdl.sepset{n,p}, engine.maximize);
%fprintf('%d sends %d\n', n, p);
msg{n,p} = normalize_pot(temp2);
end
end
% distribute from root (node to children)
for n=engine.preorder
% absorb from parents
%prod_of_msg{n} = mk_initial_pot(pot_type, doms{n}, ns, cnodes, onodes);
for p=parents(engine.tree, n)
prod_of_msg{n} = multiply_by_pot(prod_of_msg{n}, msg{p,n});
end
bel{n} = normalize_pot(multiply_pots(prod_of_msg{n}, local_kernel{n}));
% send msg to children
for c=children(engine.tree, n)
temp = divide_by_pot(prod_of_msg{n}, msg{c,n});
temp = multiply_by_pot(temp, local_kernel{n});
temp2 = marginalize_pot(temp, engine.gdl.sepset{n,c}, engine.maximize);
%fprintf('%d sends %d\n', n, c);
msg{n,c} = normalize_pot(temp2);
end
end
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