Procedure.

RandomOptimalReconciliation

1:    for each in a pre-order traversal of Gdo

2:     ifg = rt(G) then

3:      Let P denote the set .

4:      For any , assign the mapping to be s with probability .

5:   Let {g′, g″} = ChG(g).

6:   Let Q denote the set {i: bi = 1} in the context of the Equations 1, 3, or 4, used when computing N(g, s).

7:   Choose an ai, where , with probability .

8:   Assign an event type to g based on whether the chosen ai was derived from cΣ(·,·), cΔ(·,·), or cΘ(·,·).

9:   Consider the sets X′ and X″ for the chosen ai, as defined in Equation 2.

10:   Assign the mapping to be node s from X′ with probability .

11:   Assign the mapping to be node s from X″ with probability .