12,094 research outputs found
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
Fast Space Optimal Leader Election in Population Protocols
The model of population protocols refers to the growing in popularity
theoretical framework suitable for studying pairwise interactions within a
large collection of simple indistinguishable entities, frequently called
agents. In this paper the emphasis is on the space complexity in fast leader
election via population protocols governed by the random scheduler, which
uniformly at random selects pairwise interactions within the population of n
agents.
The main result of this paper is a new fast and space optimal leader election
protocol. The new protocol utilises O(log^2 n) parallel time (which is
equivalent to O(n log^2 n) sequential pairwise interactions), and each agent
operates on O(log log n) states. This double logarithmic space usage matches
asymptotically the lower bound 1/2 log log n on the minimal number of states
required by agents in any leader election algorithm with the running time
o(n/polylog n).
Our solution takes an advantage of the concept of phase clocks, a fundamental
synchronisation and coordination tool in distributed computing. We propose a
new fast and robust population protocol for initialisation of phase clocks to
be run simultaneously in multiple modes and intertwined with the leader
election process. We also provide the reader with the relevant formal
argumentation indicating that our solution is always correct, and fast with
high probability.Comment: 21 pages, 2 figures, published in SODA 2018 proceeding
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