A Fully Distributed (Minimal) Spanning Tree Algorithm

In this paper, we consider a connected undirected graph with n nodes. An asynchronous dist r ibuted algori thm is described which determines a spanning tree of the graph. Moreover, if the edges of the graph are weighted, the same algorithm can compute a minimum-weighted spanning tree. This algori thm can be favourably compared to the one of Gallagher et al. [6] in the following way: identical assumptions are made about cooperation of concurrent processes in a distributed network; we do not suppose that the weight of each edge of the g r a p h is distinct, but we assume that each node in the graph is identified by a unique integer; the number of message exchanges in our algori thm only depends on the number of nodes of the graph and not on the number of its edges; the Gallagher et al. algorithm enforces a balanced growth of intermediate subtrees which cover the nodes of the graph; our algorithm does not assume such a constraint and, hence, is more asynchronous and distributed; moreover, if we suppose that the message transmission delays as well as the speed of the different processes allow a balanced growth of the intermediate subtrees, it is shown that the number of exchanged messages is inferior to the one stated in [6]; 3n log 2 n + ( n 1) instead of 5n × log 2 n + 2E, where E is the number of edges, E > n 1. In a worst-case analysis, this number of exchanged messages is shown to be identical to the one of [6]. In a best-case analysis, our number is smaller; the description of our algorithm in a C.S.P.-like language is particularly clear and short. Therefore, we think that our algorithm can be well suited in order to implement a broadcast ing mechanism in a communicat ion network or to bui ld a communicat ion control tree allowing proper termination [5] of distributed algorithm. After having described in Section 2 our assumpt ion of the basic model of distributed network, we give an informal description of the algor i thm in Section 3 and its specification in Sect ion 4. A correctness proof of the algorithm is stated in Section 5 and its performance analysis is s tudied in Section 6. We conclude this paper by point ing out some improvements of our algori thm which could decrease the number of exchanged messages.