Parallel assignment to distinct identities in arbitrary networks

The first sequential distributed algorithm (SDA) presented to assign distinct identities to nodes in distributed systems uses the depth-first search, and requires O(n²) in communication and time complexities, where n is the number of nodes in distributed system. We present a parallel distributed algorithm (PDA) to improve the time complexity in synchronous distributed systems. This algorithm works in two phases: in the first phase, we construct a spanning tree (rooted tree) where every node knows one and only one initiator channel and, eventually a set of channels called (children channel). In the second phase, the root starts the assignation, it sends distinct identities over outgoing channels in the rooted tree. This algorithm requires O(m) messages and O(Δd) time units where Δ is an upper bound time transmission between two linked nodes, and d is the diameter of the network