Illustration of symmetry breaking in the tree algorithm for the SCE. The coagulation of mass m = m_a and m = m_b aggregates was calculated by one operation of the increase with the first term in the equation and two operations of the decrease with the second term. If m_a < m_b, the increase of m_a + m_b and the decrease of m_b were calculated with one grouping of bins (right panel), and the decrease of m_a was calculated with another grouping of bins (left panel). Since these two groupings are different, the total mass exchange is generally nonzero, which means that the total mass is not conserved at the formalization. An operation cannot be performed on the grouped (II or j) bins since it increases the number of operations, diminishing the advantage of the low computational cost of the tree method.