BATON Overlay - Restructure

Restructure

When a node x accepts a joining node y as its child and detects that the tree balance is violated, it initiates the restructuring process. Without loss of generality, suppose that this restructuring is towards the right. Assume that y joins as x's left child. To rebalance the system, x notifies y to replace its position, and notifies its right adjacent node z that x will replace z's position. z then checks its right adjacent node t to see if its left child is empty. If it is, and adding a child to t does not affect the tree balance, z takes the position of t's left child as its new position and the restructuring process stops. If t's left child is full or t cannot accept x as its left child without violating the balance property, z occupies t's position while t needs to find a new position for itself by continuing to its right adjacent node.