Computing on anonymous networks. II. Decision and membership problems

For pt I see ibid. In anonymous networks, the processors do not have identity numbers. In Part I of this paper, we characterized the classes of networks on which some representative distributed computation problems are solvable under different conditions. A new graph property called symmetricity played a central role in our analysis of anonymous networks. In Part II, we turn our attention to the computational complexity issues. We first discuss the complexity of determining the symmetricity of a given graph, and then that of testing membership in each of the 16 classes of anonymous networks defined in Part I. It turns out that, depending on the class, the complexity varies from P-time to NP-complete or co-NP-complete