8,404 research outputs found
Lossy gossip and composition of metrics
We study the monoid generated by n-by-n distance matrices under tropical (or
min-plus) multiplication. Using the tropical geometry of the orthogonal group,
we prove that this monoid is a finite polyhedral fan of dimension n(n-1)/2, and
we compute the structure of this fan for n up to 5. The monoid captures gossip
among n gossipers over lossy phone lines, and contains the gossip monoid over
ordinary phone lines as a submonoid. We prove several new results about this
submonoid, as well. In particular, we establish a sharp bound on chains of
calls in each of which someone learns something new.Comment: Minor textual edits, final versio
Consensus and Products of Random Stochastic Matrices: Exact Rate for Convergence in Probability
Distributed consensus and other linear systems with system stochastic
matrices emerge in various settings, like opinion formation in social
networks, rendezvous of robots, and distributed inference in sensor networks.
The matrices are often random, due to, e.g., random packet dropouts in
wireless sensor networks. Key in analyzing the performance of such systems is
studying convergence of matrix products . In this paper, we
find the exact exponential rate for the convergence in probability of the
product of such matrices when time grows large, under the assumption that
the 's are symmetric and independent identically distributed in time.
Further, for commonly used random models like with gossip and link failure, we
show that the rate is found by solving a min-cut problem and, hence, easily
computable. Finally, we apply our results to optimally allocate the sensors'
transmission power in consensus+innovations distributed detection
Message and time efficient multi-broadcast schemes
We consider message and time efficient broadcasting and multi-broadcasting in
wireless ad-hoc networks, where a subset of nodes, each with a unique rumor,
wish to broadcast their rumors to all destinations while minimizing the total
number of transmissions and total time until all rumors arrive to their
destination. Under centralized settings, we introduce a novel approximation
algorithm that provides almost optimal results with respect to the number of
transmissions and total time, separately. Later on, we show how to efficiently
implement this algorithm under distributed settings, where the nodes have only
local information about their surroundings. In addition, we show multiple
approximation techniques based on the network collision detection capabilities
and explain how to calibrate the algorithms' parameters to produce optimal
results for time and messages.Comment: In Proceedings FOMC 2013, arXiv:1310.459
Label-connected graphs and the gossip problem
A graph with m edges is called label-connected if the edges can be labeled with real numbers in such a way that, for every pair (u, v) of vertices, there is a (u, v)-path with ascending labels. The minimum number of edges of a label-connected graph on n vertices equals the minimum number of calls in the gossip problem for n persons, which is known to be 2n − 4 for n ≥ 4. A polynomial characterization of label-connected graphs with n vertices and 2n − 4 edges is obtained. For a graph G, let θ(G) denote the minimum number of edges that have to be added to E(G) in order to create a graph with two edge-disjoint spanning trees. It is shown that for a graph G to be label-connected, θ(G) ≤ 2 is necessary and θ(G) ≤ 1 is sufficient. For i = 1, 2, the condition θ(G) ≤ i can be checked in polynomial time. Yet recognizing label-connected graphs is an NP-complete problem. This is established by first showing that the following problem is NP-complete: Given a graph G and two vertices u and v of G, does there exist a (u, v)-path P in G such that G−E(P) is connected
Global Computation in a Poorly Connected World: Fast Rumor Spreading with No Dependence on Conductance
In this paper, we study the question of how efficiently a collection of
interconnected nodes can perform a global computation in the widely studied
GOSSIP model of communication. In this model, nodes do not know the global
topology of the network, and they may only initiate contact with a single
neighbor in each round. This model contrasts with the much less restrictive
LOCAL model, where a node may simultaneously communicate with all of its
neighbors in a single round. A basic question in this setting is how many
rounds of communication are required for the information dissemination problem,
in which each node has some piece of information and is required to collect all
others. In this paper, we give an algorithm that solves the information
dissemination problem in at most rounds in a network
of diameter , withno dependence on the conductance. This is at most an
additive polylogarithmic factor from the trivial lower bound of , which
applies even in the LOCAL model. In fact, we prove that something stronger is
true: any algorithm that requires rounds in the LOCAL model can be
simulated in rounds in the GOSSIP model. We thus
prove that these two models of distributed computation are essentially
equivalent
A trust model for spreading gossip in social networks
We introduce here a multi-type bootstrap percolation model, which we call
T-Bootstrap Percolation (T-BP), and apply it to study information propagation
in social networks. In this model, a social network is represented by a graph G
whose vertices have different labels corresponding to the type of role the
person plays in the network (e.g. a student, an educator, etc.). Once an
initial set of vertices of G is randomly selected to be carrying a gossip (e.g.
to be infected), the gossip propagates to a new vertex provided it is
transmitted by a minimum threshold of vertices with different labels. By
considering random graphs, which have been shown to closely represent social
networks, we study different properties of the T-BP model through numerical
simulations, and describe its implications when applied to rumour spread, fake
news, and marketing strategies.Comment: 9 pages, 9 figure
Highly intensive data dissemination in complex networks
This paper presents a study on data dissemination in unstructured
Peer-to-Peer (P2P) network overlays. The absence of a structure in unstructured
overlays eases the network management, at the cost of non-optimal mechanisms to
spread messages in the network. Thus, dissemination schemes must be employed
that allow covering a large portion of the network with a high probability
(e.g.~gossip based approaches). We identify principal metrics, provide a
theoretical model and perform the assessment evaluation using a high
performance simulator that is based on a parallel and distributed architecture.
A main point of this study is that our simulation model considers
implementation technical details, such as the use of caching and Time To Live
(TTL) in message dissemination, that are usually neglected in simulations, due
to the additional overhead they cause. Outcomes confirm that these technical
details have an important influence on the performance of dissemination schemes
and that the studied schemes are quite effective to spread information in P2P
overlay networks, whatever their topology. Moreover, the practical usage of
such dissemination mechanisms requires a fine tuning of many parameters, the
choice between different network topologies and the assessment of behaviors
such as free riding. All this can be done only using efficient simulation tools
to support both the network design phase and, in some cases, at runtime
Gossip on Weighted Networks
We investigate how suitable a weighted network is for gossip spreading. The
proposed model is based on the gossip spreading model introduced by Lind et.al.
on unweighted networks. Weight represents "friendship." Potential spreader
prefers not to spread if the victim of gossip is a "close friend". Gossip
spreading is related to the triangles and cascades of triangles. It gives more
insight about the structure of a network.
We analyze gossip spreading on real weighted networks of human interactions.
6 co-occurrence and 7 social pattern networks are investigated. Gossip
propagation is found to be a good parameter to distinguish co-occurrence and
social pattern networks. As a comparison some miscellaneous networks and
computer generated networks based on ER, BA, WS models are also investigated.
They are found to be quite different than the human interaction networks.Comment: 8 pages, 4 figures, 1 tabl
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