6,565 research outputs found
Finite-time Convergent Gossiping
Gossip algorithms are widely used in modern distributed systems, with
applications ranging from sensor networks and peer-to-peer networks to mobile
vehicle networks and social networks. A tremendous research effort has been
devoted to analyzing and improving the asymptotic rate of convergence for
gossip algorithms. In this work we study finite-time convergence of
deterministic gossiping. We show that there exists a symmetric gossip algorithm
that converges in finite time if and only if the number of network nodes is a
power of two, while there always exists an asymmetric gossip algorithm with
finite-time convergence, independent of the number of nodes. For nodes,
we prove that a fastest convergence can be reached in node
updates via symmetric gossiping. On the other hand, under asymmetric gossip
among nodes with , it takes at least node
updates for achieving finite-time convergence. It is also shown that the
existence of finite-time convergent gossiping often imposes strong structural
requirements on the underlying interaction graph. Finally, we apply our results
to gossip algorithms in quantum networks, where the goal is to control the
state of a quantum system via pairwise interactions. We show that finite-time
convergence is never possible for such systems.Comment: IEEE/ACM Transactions on Networking, In Pres
On the Role of Mobility for Multi-message Gossip
We consider information dissemination in a large -user wireless network in
which users wish to share a unique message with all other users. Each of
the users only has knowledge of its own contents and state information;
this corresponds to a one-sided push-only scenario. The goal is to disseminate
all messages efficiently, hopefully achieving an order-optimal spreading rate
over unicast wireless random networks. First, we show that a random-push
strategy -- where a user sends its own or a received packet at random -- is
order-wise suboptimal in a random geometric graph: specifically,
times slower than optimal spreading. It is known that this
gap can be closed if each user has "full" mobility, since this effectively
creates a complete graph. We instead consider velocity-constrained mobility
where at each time slot the user moves locally using a discrete random walk
with velocity that is much lower than full mobility. We propose a simple
two-stage dissemination strategy that alternates between individual message
flooding ("self promotion") and random gossiping. We prove that this scheme
achieves a close to optimal spreading rate (within only a logarithmic gap) as
long as the velocity is at least . The key
insight is that the mixing property introduced by the partial mobility helps
users to spread in space within a relatively short period compared to the
optimal spreading time, which macroscopically mimics message dissemination over
a complete graph.Comment: accepted to IEEE Transactions on Information Theory, 201
Information Gathering in Ad-Hoc Radio Networks with Tree Topology
We study the problem of information gathering in ad-hoc radio networks
without collision detection, focussing on the case when the network forms a
tree, with edges directed towards the root. Initially, each node has a piece of
information that we refer to as a rumor. Our goal is to design protocols that
deliver all rumors to the root of the tree as quickly as possible. The protocol
must complete this task within its allotted time even though the actual tree
topology is unknown when the computation starts. In the deterministic case,
assuming that the nodes are labeled with small integers, we give an O(n)-time
protocol that uses unbounded messages, and an O(n log n)-time protocol using
bounded messages, where any message can include only one rumor. We also
consider fire-and-forward protocols, in which a node can only transmit its own
rumor or the rumor received in the previous step. We give a deterministic
fire-and- forward protocol with running time O(n^1.5), and we show that it is
asymptotically optimal. We then study randomized algorithms where the nodes are
not labelled. In this model, we give an O(n log n)-time protocol and we prove
that this bound is asymptotically optimal
Relational aggressionan overview of the complicated behaviors of girls
Includes bibliographical references
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