91,746 research outputs found
Termination Detection of Local Computations
Contrary to the sequential world, the processes involved in a distributed
system do not necessarily know when a computation is globally finished. This
paper investigates the problem of the detection of the termination of local
computations. We define four types of termination detection: no detection,
detection of the local termination, detection by a distributed observer,
detection of the global termination. We give a complete characterisation
(except in the local termination detection case where a partial one is given)
for each of this termination detection and show that they define a strict
hierarchy. These results emphasise the difference between computability of a
distributed task and termination detection. Furthermore, these
characterisations encompass all standard criteria that are usually formulated :
topological restriction (tree, rings, or triangu- lated networks ...),
topological knowledge (size, diameter ...), and local knowledge to distinguish
nodes (identities, sense of direction). These results are now presented as
corollaries of generalising theorems. As a very special and important case, the
techniques are also applied to the election problem. Though given in the model
of local computations, these results can give qualitative insight for similar
results in other standard models. The necessary conditions involve graphs
covering and quasi-covering; the sufficient conditions (constructive local
computations) are based upon an enumeration algorithm of Mazurkiewicz and a
stable properties detection algorithm of Szymanski, Shi and Prywes
Leader Election for Anonymous Asynchronous Agents in Arbitrary Networks
We study the problem of leader election among mobile agents operating in an
arbitrary network modeled as an undirected graph. Nodes of the network are
unlabeled and all agents are identical. Hence the only way to elect a leader
among agents is by exploiting asymmetries in their initial positions in the
graph. Agents do not know the graph or their positions in it, hence they must
gain this knowledge by navigating in the graph and share it with other agents
to accomplish leader election. This can be done using meetings of agents, which
is difficult because of their asynchronous nature: an adversary has total
control over the speed of agents. When can a leader be elected in this
adversarial scenario and how to do it? We give a complete answer to this
question by characterizing all initial configurations for which leader election
is possible and by constructing an algorithm that accomplishes leader election
for all configurations for which this can be done
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