For each non-leaf node n in a preferred path P, it has a non-preferred child c, which is the root of a new auxiliary tree.

For each node n between w and e:

Each node n is a switch which may be' on'or'off', 1 or 0.

Select the node n whose distance d from this input is least.

The depth of a node n is the length of the path from the root to the node.

Case 1: The current node N is at the root of the tree.

Independently, it performs the same procedure starting at node N and going in reverse order.

Then, node n and n' belongs to same fragment (so the edge is not outgoing).

Then, node n and n' belongs to the different fragments (so the edge is outgoing).

This arises on slot t for node n and commodity c if: