  We consider asynchronous message-passing systems in which some links are
timely and processes may crash. Each run defines a timeliness graph among
correct processes: (p; q) is an edge of the timeliness graph if the link from p
to q is timely (that is, there is bound on communication delays from p to q).
The main goal of this paper is to approximate this timeliness graph by graphs
having some properties (such as being trees, rings, ...). Given a family S of
graphs, for runs such that the timeliness graph contains at least one graph in
S then using an extraction algorithm, each correct process has to converge to
the same graph in S that is, in a precise sense, an approximation of the
timeliness graph of the run. For example, if the timeliness graph contains a
ring, then using an extraction algorithm, all correct processes eventually
converge to the same ring and in this ring all nodes will be correct processes
and all links will be timely. We first present a general extraction algorithm
and then a more specific extraction algorithm that is communication efficient
(i.e., eventually all the messages of the extraction algorithm use only links
of the extracted graph).
