26,461 research outputs found
Stabilizing leader election in population protocols
In this paper we address the stabilizing leader election problem in the population protocols model augmented with oracles. Population protocols is a recent model of computation that captures the interactions of biological systems. In this model emergent global behavior is observed while anonymous finite-state agents(nodes) perform local peer interactions. Uniform self-stabilizing leader election is impossible in such systems without additional assumptions. Therefore, the classical model has been augmented with the eventual leader detector, Omega?, that eventually detects the presence or absence of a leader. In the augmented model several solutions for leader election in rings and complete networks have been proposed. In this work we extend the study to trees and arbitrary topologies. We propose deterministic and probabilistic solutions. All the proposed algorithms are memory optimal --- they need only one memory bit per agent. Additionally, we prove the necessity of the eventual leader detector even in environments helped by randomization
Leader Election in Anonymous Rings: Franklin Goes Probabilistic
We present a probabilistic leader election algorithm for anonymous, bidirectional, asynchronous rings. It is based on an algorithm from Franklin, augmented with random identity selection, hop counters to detect identity clashes, and round numbers modulo 2. As a result, the algorithm is finite-state, so that various model checking techniques can be employed to verify its correctness, that is, eventually a unique leader is elected with probability one. We also sketch a formal correctness proof of the algorithm for rings with arbitrary size
Self-stabilizing Leader Election in Population Protocols over Arbitrary Communication Graphs
This paper considers the fundamental problem of \emph{self-stabilizing leader election} () in the model of \emph{population protocols}. In this model, an unknown number of asynchronous, anonymous and finite state mobile agents interact in pairs over a given communication graph. has been shown to be impossible in the original model. This impossibility can been circumvented by a modular technique augmenting the system with an \emph{oracle} - an external module abstracting the added assumption about the system. Fischer and Jiang have proposed solutions to , for complete communication graphs and rings, using an oracle , called the \emph{eventual leader detector}. In this work, we present a solution for arbitrary graphs, using a \emph{composition} of two copies of . We also prove that the difficulty comes from the requirement of self-stabilization, by giving a solution without oracle for arbitrary graphs, when an uniform initialization is allowed. Finally, we prove that there is no self-stabilizing \emph{implementation} of using , in a sense we define precisely
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
Compact Deterministic Self-Stabilizing Leader Election: The Exponential Advantage of Being Talkative
This paper focuses on compact deterministic self-stabilizing solutions for
the leader election problem. When the protocol is required to be \emph{silent}
(i.e., when communication content remains fixed from some point in time during
any execution), there exists a lower bound of Omega(\log n) bits of memory per
node participating to the leader election (where n denotes the number of nodes
in the system). This lower bound holds even in rings. We present a new
deterministic (non-silent) self-stabilizing protocol for n-node rings that uses
only O(\log\log n) memory bits per node, and stabilizes in O(n\log^2 n) rounds.
Our protocol has several attractive features that make it suitable for
practical purposes. First, the communication model fits with the model used by
existing compilers for real networks. Second, the size of the ring (or any
upper bound on this size) needs not to be known by any node. Third, the node
identifiers can be of various sizes. Finally, no synchrony assumption, besides
a weakly fair scheduler, is assumed. Therefore, our result shows that, perhaps
surprisingly, trading silence for exponential improvement in term of memory
space does not come at a high cost regarding stabilization time or minimal
assumptions
Memory lower bounds for deterministic self-stabilization
In the context of self-stabilization, a \emph{silent} algorithm guarantees
that the register of every node does not change once the algorithm has
stabilized. At the end of the 90's, Dolev et al. [Acta Inf. '99] showed that,
for finding the centers of a graph, for electing a leader, or for constructing
a spanning tree, every silent algorithm must use a memory of
bits per register in -node networks. Similarly, Korman et al. [Dist. Comp.
'07] proved, using the notion of proof-labeling-scheme, that, for constructing
a minimum-weight spanning trees (MST), every silent algorithm must use a memory
of bits per register. It follows that requiring the algorithm
to be silent has a cost in terms of memory space, while, in the context of
self-stabilization, where every node constantly checks the states of its
neighbors, the silence property can be of limited practical interest. In fact,
it is known that relaxing this requirement results in algorithms with smaller
space-complexity.
In this paper, we are aiming at measuring how much gain in terms of memory
can be expected by using arbitrary self-stabilizing algorithms, not necessarily
silent. To our knowledge, the only known lower bound on the memory requirement
for general algorithms, also established at the end of the 90's, is due to
Beauquier et al.~[PODC '99] who proved that registers of constant size are not
sufficient for leader election algorithms. We improve this result by
establishing a tight lower bound of bits per
register for self-stabilizing algorithms solving -coloring or
constructing a spanning tree in networks of maximum degree~. The lower
bound bits per register also holds for leader election
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
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