1,493 research outputs found
Robust Leader Election in a Fast-Changing World
We consider the problem of electing a leader among nodes in a highly dynamic
network where the adversary has unbounded capacity to insert and remove nodes
(including the leader) from the network and change connectivity at will. We
present a randomized Las Vegas algorithm that (re)elects a leader in O(D\log n)
rounds with high probability, where D is a bound on the dynamic diameter of the
network and n is the maximum number of nodes in the network at any point in
time. We assume a model of broadcast-based communication where a node can send
only 1 message of O(\log n) bits per round and is not aware of the receivers in
advance. Thus, our results also apply to mobile wireless ad-hoc networks,
improving over the optimal (for deterministic algorithms) O(Dn) solution
presented at FOMC 2011. We show that our algorithm is optimal by proving that
any randomized Las Vegas algorithm takes at least omega(D\log n) rounds to
elect a leader with high probability, which shows that our algorithm yields the
best possible (up to constants) termination time.Comment: In Proceedings FOMC 2013, arXiv:1310.459
Improved Tradeoffs for Leader Election
We consider leader election in clique networks, where nodes are connected
by point-to-point communication links. For the synchronous clique under
simultaneous wake-up, i.e., where all nodes start executing the algorithm in
round , we show a tradeoff between the number of messages and the amount of
time. More specifically, we show that any deterministic algorithm with a
message complexity of requires rounds, for . Our result holds even if
the node IDs are chosen from a relatively small set of size ,
as we are able to avoid using Ramsey's theorem. We also give an upper bound
that improves over the previously-best tradeoff. Our second contribution for
the synchronous clique under simultaneous wake-up is to show that is in fact a lower bound on the message complexity that holds for any
deterministic algorithm with a termination time . We complement this
result by giving a simple deterministic algorithm that achieves leader election
in sublinear time while sending only messages, if the ID space is
of at most linear size. We also show that Las Vegas algorithms (that never
fail) require messages. For the synchronous clique under
adversarial wake-up, we show that is a tight lower bound for
randomized -round algorithms. Finally, we turn our attention to the
asynchronous clique: Assuming adversarial wake-up, we give a randomized
algorithm that achieves a message complexity of and an
asynchronous time complexity of . For simultaneous wake-up, we translate
the deterministic tradeoff algorithm of Afek and Gafni to the asynchronous
model, thus partially answering an open problem they pose
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