This paper addresses the consensus problem in homonymous distributed systems
where processes are prone to crash failures and have no initial knowledge of
the system membership ("homonymous" means that several processes may have the
same identifier). New classes of failure detectors suited to these systems are
first defined. Among them, the classes H\Omega\ and H\Sigma\ are introduced
that are the homonymous counterparts of the classes \Omega\ and \Sigma,
respectively.
In this paper we present an algorithm, called conauto-2.0, that can
efficiently compute a set of generators of the automorphism group of a graph,
and test whether two graphs are isomorphic, finding an isomorphism if they are.
This algorithm uses the basic individualization/refinement technique, and is an
improved version of the algorithm conauto, which has been shown to be very fast
for random graphs and several families of hard graphs.
Sampling a large network with a given distribution has been identified as a
useful operation to build network overlays. For example, sampling nodes with
uniform probability is the cornerstone of epidemic information spreading, and
constructing small world network topologies can be done by sampling with a
probability that depends on the distance to a given node. In this paper we
describe distributed algorithms for sampling networks, so that a node is
selected with a probability that is a function of the distance of the node to a
special node, called the \emph{source}.