A Communication-Efficient Self-stabilizing Algorithm for Breadth-First Search Trees

A self-stabilizing algorithm converges to its designated behavior from an arbitrary initial configuration. It is standard to assume that each process maintains communication with all its neighbors. We consider the problem of self-stabilizing construction of a breadth first search (BFS) tree in a connected network of processes, and consider algorithms which are not given the size of the network, nor even an upper bound on that size. It is known that an algorithm that constructs a BFS tree must allow communication across every edge, but not necessarily in both directions. If m is the number of undirected edges, and hence the number of directed edges is 2m, then every self-stabilizing BFS tree algorithm must allow perpetual communication across at least m directed edges. We present an algorithm with reduced communication for the BFS tree problem in a network with unique identifiers and a designated root. In this algorithm, communication across all channels is permitted during a finite prefix of a computation, but there is a reduced set of directed edges across which communication is allowed forever. After a finite prefix, the algorithm uses only m + n - 1 directed edges for communication, where n is the number of processes in the network and m is the number of edges.