Distributed algorithms for constructing a minimum-weight spanning tree in a broadcast network

AbstractTwo distributed algorithms are presented for a network using a common communication channel (e.g. radio) in which all nodes are within signal range and in line of sight of each other: (a) an algorithm to compute all $$\left( {\begin{array}{*{20}c} N \\ 2 \\ \end{array} } \right)$$ internode distances (in terms of propagation delays) in the network. the algorithm requires only 2 messages per node, and provides each node with the distances to all other nodes. (b) An algorithm for constructing a minimum-weight spanning tree (MST) in such a network. This algorithm starts out with the information provided by (a) and ends with each node possessing the explicit knowledge of the full MST. The algorithm requires at most log2N messages per node. The internal processing in each node needsO(N logN) time andO(N) space. All messages required by (a) and (b) contain at most one edge weight plus 2 log2N bits. Some possible applications of the algorithms are: position-location, tuning acknowledgement time-out mechanisms, tuning the scheduling functions of access protocols that are sensitive to individual internode propagation delays, and selecting performance effective transmission sequences for round robin access protocols.