841 research outputs found
The robustness of democratic consensus
In linear models of consensus dynamics, the state of the various agents
converges to a value which is a convex combination of the agents' initial
states. We call it democratic if in the large scale limit (number of agents
going to infinity) the vector of convex weights converges to 0 uniformly.
Democracy is a relevant property which naturally shows up when we deal with
opinion dynamic models and cooperative algorithms such as consensus over a
network: it says that each agent's measure/opinion is going to play a
negligeable role in the asymptotic behavior of the global system. It can be
seen as a relaxation of average consensus, where all agents have exactly the
same weight in the final value, which becomes negligible for a large number of
agents.Comment: 13 pages, 2 fig
Active Phase for Activated Random Walks on the Lattice in all Dimensions
We show that the critical density of the Activated Random Walk model on
is strictly less than one when the sleep rate is small
enough, and tends to when , in any dimension .
As far as we know, the result is new for .
We prove this by showing that, for high enough density and small enough sleep
rate, the stabilization time of the model on the -dimensional torus is
exponentially large. To do so, we fix the the set of sites where the particles
eventually fall asleep, which reduces the problem to a simpler model with
density one. Taking advantage of the Abelian property of the model, we show
that the stabilization time stochastically dominates the escape time of a
one-dimensional random walk with a negative drift. We then check that this slow
phase for the finite volume dynamics implies the existence of an active phase
on the infinite lattice.Comment: 27 pages, new version with minor correction
Choice and bias in random walks
We analyse the following random walk process inspired by the power-of-two-choice paradigm: starting from a given vertex, at each step, unlike the simple random walk (SRW) that always moves to a randomly chosen neighbour, we have the choice between two uniformly and independently chosen neighbours. We call this process the choice random walk (CRW). We first prove that for any graph, there is a strategy for the CRW that visits any given vertex in expected tim
Storage and Search in Dynamic Peer-to-Peer Networks
We study robust and efficient distributed algorithms for searching, storing,
and maintaining data in dynamic Peer-to-Peer (P2P) networks. P2P networks are
highly dynamic networks that experience heavy node churn (i.e., nodes join and
leave the network continuously over time). Our goal is to guarantee, despite
high node churn rate, that a large number of nodes in the network can store,
retrieve, and maintain a large number of data items. Our main contributions are
fast randomized distributed algorithms that guarantee the above with high
probability (whp) even under high adversarial churn:
1. A randomized distributed search algorithm that (whp) guarantees that
searches from as many as nodes ( is the stable network size)
succeed in -rounds despite churn, for
any small constant , per round. We assume that the churn is
controlled by an oblivious adversary (that has complete knowledge and control
of what nodes join and leave and at what time, but is oblivious to the random
choices made by the algorithm).
2. A storage and maintenance algorithm that guarantees (whp) data items can
be efficiently stored (with only copies of each data item)
and maintained in a dynamic P2P network with churn rate up to
per round. Our search algorithm together with our
storage and maintenance algorithm guarantees that as many as nodes
can efficiently store, maintain, and search even under churn per round. Our algorithms require only polylogarithmic in bits to
be processed and sent (per round) by each node.
To the best of our knowledge, our algorithms are the first-known,
fully-distributed storage and search algorithms that provably work under highly
dynamic settings (i.e., high churn rates per step).Comment: to appear at SPAA 201
Capacity Proportional Unstructured Peer-to-Peer Networks
Existing methods to utilize capacity-heterogeneity in a P2P system either rely
on constructing special overlays with capacity-proportional node degree or use topology adaptation to match a node's capacity with that of its neighbors. In existing
P2P networks, which are often characterized by diverse node capacities and high
churn, these methods may require large node degree or continuous topology adaptation, potentially making them infeasible due to their high overhead. In this thesis,
we propose an unstructured P2P system that attempts to address these issues. We
first prove that the overall throughput of search queries in a heterogeneous network
is maximized if and only if traffic load through each node is proportional to its capacity. Our proposed system achieves this traffic distribution by biasing search walks
using the Metropolis-Hastings algorithm, without requiring any special underlying
topology. We then define two saturation metrics for measuring the performance of
overlay networks: one for quantifying their ability to support random walks and the
second for measuring their potential to handle the overhead caused by churn. Using
simulations, we finally compare our proposed method with Gia, an existing system
which uses topology adaptation, and find that the former performs better under all
studied conditions, both saturation metrics, and such end-to-end parameters as query
success rate, latency, and query-hits for various file replication schemes
Gossip Algorithms for Distributed Signal Processing
Gossip algorithms are attractive for in-network processing in sensor networks
because they do not require any specialized routing, there is no bottleneck or
single point of failure, and they are robust to unreliable wireless network
conditions. Recently, there has been a surge of activity in the computer
science, control, signal processing, and information theory communities,
developing faster and more robust gossip algorithms and deriving theoretical
performance guarantees. This article presents an overview of recent work in the
area. We describe convergence rate results, which are related to the number of
transmitted messages and thus the amount of energy consumed in the network for
gossiping. We discuss issues related to gossiping over wireless links,
including the effects of quantization and noise, and we illustrate the use of
gossip algorithms for canonical signal processing tasks including distributed
estimation, source localization, and compression.Comment: Submitted to Proceedings of the IEEE, 29 page
A survey of distributed data aggregation algorithms
Distributed data aggregation is an important task, allowing the decentralized determination of meaningful global properties, which can then be used to direct the execution of other applications. The resulting values are derived by the distributed computation of functions like COUNT, SUM, and AVERAGE. Some application examples deal with the determination of the network size, total storage capacity, average load, majorities and many others. In the last decade, many different approaches have been proposed, with different trade-offs in terms of accuracy, reliability, message and time complexity. Due to the considerable amount and variety of aggregation algorithms, it can be difficult and time consuming to determine which techniques will be more appropriate to use in specific settings, justifying the existence of a survey to aid in this task. This work reviews the state of the art on distributed data aggregation algorithms, providing three main contributions. First, it formally defines the concept of aggregation, characterizing the different types of aggregation functions. Second, it succinctly describes the main aggregation techniques, organizing them in a taxonomy. Finally, it provides some guidelines toward the selection and use of the most relevant techniques, summarizing their principal characteristics.info:eu-repo/semantics/publishedVersio
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