Algorithm 3. Pseudocode of the binary label assignment procedure.

Procedure: AssignBinaryLabels(RootNode, MaxRings, K) Input: RootNode: coordinator node, MaxRings: maximum number of rings, K: branching factor per node Output: LabelMap: mapping from each node to its full binary label (InterID + IntraID) Initialize Queue ← [RootNode] Set LabelMap[RootNode] ← “000000”  // k bits InterID + 2 bits IntraID Set RingLevel[RootNode] ← 0 While Queue is not empty:    Parent ← Queue.dequeue()    ParentLabel ← LabelMap[Parent]    CurrentRing ← RingLevel[Parent] + 1    If CurrentRing ≤ MaxRings then       For i from 1 to K do          Child ← GenerateChildNode(Parent, i)           If Child ≠ null then               InterID ← Binary(CurrentRing, k) // fixed k bits               IntraID ← Binary(i, 2) // fixed 2 bits                   Label ← InterID + IntraID                   LabelMap[Child] ← Label                   RingLevel[Child] ← CurrentRing                   Queue.enqueue(Child)           end if       end for    end if end while Return LabelMap