A distributed algorithm for constructing an Eulerian tour

We present an efficient distributed algorithm for constructing an Eulerian tour in a network. To construct an Eulerian circuit the algorithm requires (1+r)(|E||V|) messages and time units, where |E| is the number of the communication links, |V| is the number of the nodes in the underlying network graph, and 0⩽r<1. The value of r depends on the network topology and on the chosen traversal path. In the best case, when r=0 the algorithm only requires (|E|+|V|) messages and time units. A simple modification allows us to construct a (noncyclic) tour using (1+r)(|E|+2|V|) messages and time units