A new node-join-tree distributed algorithm for minimum weight spanning trees

A distributed algorithm that uses a node-join-tree approach for the minimum-spanning-tree problem in a communication network is developed. The algorithm needs at most (2e+n(n-1)/4) messages in O(n² ) time on a general random graph. In the best case, it needs only 2e messages in O(log n) time. The parameters e and n are the number of edges and nodes, respectively. Although the worst-case performance is not better than that of tree-join-tree algorithms under some extreme cases, simulation results show that it provides better performance in most cases. The algorithm is initialized from a single node, so that there is no need to wake up all nodes at the beginning. It is less complicated than other algorithms, so that a reliable implementation is easier to achieve. The results can be used to improve the algorithms for many other problems in distributed computing, such as leader-election, node-counting, deadlock-resolution, and message-broadcasting