17 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
Time vs. Information Tradeoffs for Leader Election in Anonymous Trees
The leader election task calls for all nodes of a network to agree on a
single node. If the nodes of the network are anonymous, the task of leader
election is formulated as follows: every node of the network must output a
simple path, coded as a sequence of port numbers, such that all these paths end
at a common node, the leader. In this paper, we study deterministic leader
election in anonymous trees.
Our aim is to establish tradeoffs between the allocated time and the
amount of information that has to be given to the nodes to
enable leader election in time in all trees for which leader election in
this time is at all possible. Following the framework of , this information (a single binary string) is provided to all
nodes at the start by an oracle knowing the entire tree. The length of this
string is called the . For an allocated time ,
we give upper and lower bounds on the minimum size of advice sufficient to
perform leader election in time .
We consider -node trees of diameter . While leader election
in time can be performed without any advice, for time we give
tight upper and lower bounds of . For time we give
tight upper and lower bounds of for even values of ,
and tight upper and lower bounds of for odd values of .
For the time interval for constant ,
we prove an upper bound of and a lower bound of
, the latter being valid whenever is odd or when
the time is at most . Finally, for time for any
constant (except for the case of very small diameters), we give
tight upper and lower bounds of
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