58,668 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
Efficient size estimation and impossibility of termination in uniform dense population protocols
We study uniform population protocols: networks of anonymous agents whose
pairwise interactions are chosen at random, where each agent uses an identical
transition algorithm that does not depend on the population size . Many
existing polylog time protocols for leader election and majority
computation are nonuniform: to operate correctly, they require all agents to be
initialized with an approximate estimate of (specifically, the exact value
). Our first main result is a uniform protocol for
calculating with high probability in time and
states ( bits of memory). The protocol is
converging but not terminating: it does not signal when the estimate is close
to the true value of . If it could be made terminating, this would
allow composition with protocols, such as those for leader election or
majority, that require a size estimate initially, to make them uniform (though
with a small probability of failure). We do show how our main protocol can be
indirectly composed with others in a simple and elegant way, based on the
leaderless phase clock, demonstrating that those protocols can in fact be made
uniform. However, our second main result implies that the protocol cannot be
made terminating, a consequence of a much stronger result: a uniform protocol
for any task requiring more than constant time cannot be terminating even with
probability bounded above 0, if infinitely many initial configurations are
dense: any state present initially occupies agents. (In particular,
no leader is allowed.) Crucially, the result holds no matter the memory or time
permitted. Finally, we show that with an initial leader, our size-estimation
protocol can be made terminating with high probability, with the same
asymptotic time and space bounds.Comment: Using leaderless phase cloc
Exploiting spontaneous transmissions for broadcasting and leader election in radio networks
We study two fundamental communication primitives: broadcasting and leader election in the classical model of multi-hop radio networks with unknown topology and without collision detection mechanisms. It has been known for almost 20 years that in undirected networks with n nodes and diameter D, randomized broadcasting requires Ω(D log n/D + log2 n) rounds, assuming that uninformed nodes are not allowed to communicate (until they are informed). Only very recently, Haeupler and Wajc (PODC'2016) showed that this bound can be improved for the model with spontaneous transmissions, providing an O(D log n log log n/log D + logO(1) n)-time broadcasting algorithm. In this article, we give a new and faster algorithm that completes broadcasting in O(D log n/log D + logO(1) n) time, succeeding with high probability. This yields the first optimal O(D)-time broadcasting algorithm whenever n is polynomial in D.
Furthermore, our approach can be applied to design a new leader election algorithm that matches the performance of our broadcasting algorithm. Previously, all fast randomized leader election algorithms have used broadcasting as a subroutine and their complexity has been asymptotically strictly larger than the complexity of broadcasting. In particular, the fastest previously known randomized leader election algorithm of Ghaffari and Haeupler (SODA'2013) requires O(D log n/D min {log log n, log n/D} + logO(1) n)-time, succeeding with high probability. Our new algorithm again requires O(D log n/log D + logO(1) n) time, also succeeding with high probability
Gossip in a Smartphone Peer-to-Peer Network
In this paper, we study the fundamental problem of gossip in the mobile
telephone model: a recently introduced variation of the classical telephone
model modified to better describe the local peer-to-peer communication services
implemented in many popular smartphone operating systems. In more detail, the
mobile telephone model differs from the classical telephone model in three
ways: (1) each device can participate in at most one connection per round; (2)
the network topology can undergo a parameterized rate of change; and (3)
devices can advertise a parameterized number of bits about their state to their
neighbors in each round before connection attempts are initiated. We begin by
describing and analyzing new randomized gossip algorithms in this model under
the harsh assumption of a network topology that can change completely in every
round. We prove a significant time complexity gap between the case where nodes
can advertise bits to their neighbors in each round, and the case where
nodes can advertise bit. For the latter assumption, we present two
solutions: the first depends on a shared randomness source, while the second
eliminates this assumption using a pseudorandomness generator we prove to exist
with a novel generalization of a classical result from the study of two-party
communication complexity. We then turn our attention to the easier case where
the topology graph is stable, and describe and analyze a new gossip algorithm
that provides a substantial performance improvement for many parameters. We
conclude by studying a relaxed version of gossip in which it is only necessary
for nodes to each learn a specified fraction of the messages in the system.Comment: Extended Abstract to Appear in the Proceedings of the ACM Conference
on the Principles of Distributed Computing (PODC 2017
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