  Self-stabilization for non-masking fault-tolerant distributed system has
received considerable research interest over the last decade. In this paper, we
propose a self-stabilizing algorithm for 2-edge-connectivity and
2-vertex-connectivity of an asynchronous distributed computer network. It is
based on a self-stabilizing depth-first search, and is not a composite
algorithm in the sense that it is not composed of a number of self-stabilizing
algorithms that run concurrently. The time and space complexities of the
algorithm are the same as those of the underlying self-stabilizing depth-first
search algorithm which are O(dn\Delta) rounds and O(n\log \Delta) bits per
processor, respectively, where \Delta (<= n) is an upper bound on the degree of
a node, d (<= n) is the diameter of the graph, and n is the number of nodes in
the network.
