160 research outputs found
Gossiping in chordal rings under the line model
The line model assumes long distance
calls between non neighboring processors. In this sense, the line
model is strongly related to circuit-switched networks, wormhole
routing, optical networks supporting wavelength division
multiplexing, ATM switching, and networks supporting connected mode
routing protocols.
Since the chordal rings are competitors of networks as meshes or
tori because of theirs short diameter and bounded degree, it is of
interest to ask whether they can support intensive communications
(typically all-to-all) as efficiently as these networks. We
propose polynomial algorithms to derive optimal or near optimal
gossip protocols in the chordal ring
Lower bounds on systolic gossip
AbstractGossiping is an extensively investigated information dissemination process in which each processor has a distinct item of information and has to collect all the items possessed by the other processors. In this paper we provide an innovative and general lower bound technique relying on the novel notion of delay digraph of a gossiping protocol and on the use of matrix norm methods. Such a technique is very powerful and allows the determination of new and significantly improved lower bounds in many cases. In fact, we derive the first general lower bound on the gossiping time of systolic protocols, i.e., constituted by a periodic repetition of simple communication steps. In particular, given any network of n processors and any systolic period s, in the directed and the undirected half-duplex cases every s-systolic gossip protocol takes at least log(n)/log(1/λ)−O(loglog(n)) time steps, where λ is the unique solution between 0 and 1 of λ·p⌊s/2⌋(λ)·p⌈s/2⌉(λ)=1, with pi(λ)=1+λ2+⋯+λ2i−2 for any integer i>0. We then provide improved lower bounds in the directed and half-duplex cases for many well-known network topologies, such as Butterfly, de Bruijn, and Kautz graphs. All the results are extended also to the full-duplex case. Our technique is very general, as for s→∞ it allows the determination of improved results even for non-systolic protocols. In fact, for general networks, as a simple corollary it yields a lower bound only an O(loglog(n)) additive factor far from the general one independently proved in [Proc. 1st ACM Symposium on Parallel Algorithms and Architectures (SPAA), 1989, p. 318; Topics in Combinatorics and Graph Theory (1990) 451; SIAM Journal on Computing 21(1) (1992) 111; Discrete Applied Mathematics 42 (1993) 75] for all graphs and any (non-systolic) gossip protocol. Moreover, for specific networks, it significantly improves with respect to the previously known results, even in the full-duplex case. Correspondingly, better lower bounds on the gossiping time of non-systolic protocols are determined in the directed, half-duplex and full-duplex cases for Butterfly, de Bruijn, and Kautz graphs. Even if in this paper we give only a limited number of examples, our technique has wide applicability and gives a general framework that often allows to get improved lower bounds on the gossiping time of systolic and non-systolic protocols in the directed, half-duplex and full-duplex cases
A survey of flooding, gossip routing, and related schemes for wireless multi- hop networks
Flooding is an essential and critical service in computer networks that is
used by many routing protocols to send packets from a source to all nodes in
the network. As the packets are forwarded once by each receiving node, many
copies of the same packet traverse the network which leads to high redundancy
and unnecessary usage of the sparse capacity of the transmission medium.
Gossip routing is a well-known approach to improve the flooding in wireless
multi-hop networks. Each node has a forwarding probability p that is either
statically per-configured or determined by information that is available at
runtime, e.g, the node degree. When a packet is received, the node selects a
random number r. If the number r is below p, the packet is forwarded and
otherwise, in the most simple gossip routing protocol, dropped. With this
approach the redundancy can be reduced while at the same time the reachability
is preserved if the value of the parameter p (and others) is chosen with
consideration of the network topology. This technical report gives an overview
of the relevant publications in the research domain of gossip routing and
gives an insight in the improvements that can be achieved. We discuss the
simulation setups and results of gossip routing protocols as well as further
improved flooding schemes. The three most important metrics in this
application domain are elaborated: reachability, redundancy, and management
overhead. The published studies used simulation environments for their
research and thus the assumptions, models, and parameters of the simulations
are discussed and the feasibility of an application for real world wireless
networks are highlighted. Wireless mesh networks based on IEEE 802.11 are the
focus of this survey but publications about other network types and
technologies are also included. As percolation theory, epidemiological models,
and delay tolerant networks are often referred as foundation, inspiration, or
application of gossip routing in wireless networks, a brief introduction to
each research domain is included and the applicability of the particular
models for the gossip routing is discussed
Circuit-Switched Gossiping in the 3-Dimensional Torus Networks
In this paper we describe, in the case of short messages, an efficient gossiping algorithm for 3-dimensional torus networks (wrap-around or toroidal meshes) that uses synchronous circuit-switched routing. The algorithm is based on a recursive decomposition of a torus. The algorithm requires an optimal number of rounds and a quasi-optimal number of intermediate switch settings to gossip in an torus
Minimal contention-free matrices with application to multicasting
In this paper, we show that the multicast problem in trees can be
expressed in term of arranging rows and columns of boolean matrices.
Given a matrix with 0-1 entries, the {\em shadow}
of is defined as a boolean vector of entries such that
if and only if there is no 1-entry in the th column of
, and otherwise. (The shadow can also be seen as the
binary expression of the integer .
Similarly, every row of can be seen as the binary expression of
an integer.) According to this formalism, the key for solving a
multicast problem in trees is shown to be the following. Given a matrix with 0-1 entries, finding a matrix such
that:
1- has at most one 1-entry per column;
2- every row of (viewed as the binary expression of
an integer) is larger than the corresponding row of , ; and
3- the shadow of (viewed as an integer) is minimum.
We show that there is an algorithm that
returns for any boolean matrix .
The application of this result is the following: Given a {\em directed}
tree whose arcs are oriented from the root toward the leaves,
and a subset of nodes , there exists a polynomial-time algorithm
that computes an optimal multicast protocol from the root to all
nodes of in the all-port line model.Peer Reviewe
Consensus Algorithms for Estimation and Discrete Averaging in Networked Control Systems
In this thesis several topics on consensus and gossip algorithms for multi-agent systems are addressed. An agent is a dynamical system that can be fully described by a state-space representation of its dynamics. A multi-agent system is a network of agents whose pattern of interactions or couplings is described by a graph. Consensus problems in multi-agent systems consist in the study of local interaction rules between the agents such that as global emergent behavior the network converges to the so called "consensus" or "agreement" state where the value of each agent's state is the same and it is possibly a function of the initial network state, for instance the average. A consensus algorithm is thus a set of local interaction rules that solve the consensus problem under some assumptions on the network topology.
A gossip algorithm is a set of local state update rules between the agents that, disregarding their objective, are supposed to be implemented in a totally asynchronous way between pairs of neighboring agents, thus resembling the act of "gossiping" in a crowd of people.
In this thesis several algorithms based on gossip that solve the consensus and other related problems are presented.
In the �first part, several solutions to the consensus problem based on gossip under different sets of assumptions are proposed. In the fi�rst case, it is assumed that the state of the agents is discretized and represents a collection of tasks of different size. In the second case,
under the same discretization assumptions of the �rst case, it is assumed that the network is represented by a Hamiltonian graph and it is shown how under this assumption the convergence speed can be improved. In the third case, a solution for the consensus problem for networks represented by arbitrary strongly connected directed graphs is proposed, assuming that the state of the agents is a real number.
In the fourth case, a coordinate-free consensus algorithm based on gossip is designed and applied to a network of vehicles able to sense the relative distance between each other but with no access to absolute position information or to a common coordinate system. The proposed algorithm is then used to build in a decentralized way a common reference frame for the network of vehicles.
In the second part, a novel local interaction rule based on the consensus equation is proposed together with an algorithm to estimate in a decentralized way the spectrum of the Laplacian matrix that encodes the network topology. As emergent behavior, each agent's state oscillates only at frequencies corresponding to the eigenvalues of the
Laplacian matrix thus mapping the spectrum estimation problem into a signal processing problem solvable using the Fourier Transform. It is further shown that the constant component of the emergent behavior in the frequency domain solves the consensus on the average problem.
The spectrum estimation algorithm is then applied to leader-follower networks of mobile vehicles to infer in a decentralized way properties such as controllability, osservability and other topological features of
the network such as its topology.
Finally, a fault detection and recovery technique for sensor networks based on the so called motion-probes is presented to address the inherent lack of robustness against outlier agents in networks implementing
consensus algorithms to solve the distributed averaging problem
Efficient Information Aggregation Strategies for Distributed Control and Signal Processing
This thesis is concerned with distributed control and coordination of
networks consisting of multiple, potentially mobile, agents. This is motivated
mainly by the emergence of large scale networks characterized by the lack of
centralized access to information and time-varying connectivity. Control and
optimization algorithms deployed in such networks should be completely
distributed, relying only on local observations and information, and robust
against unexpected changes in topology such as link failures. We will describe
protocols to solve certain control and signal processing problems in this
setting. We will demonstrate that a key challenge for such systems is the
problem of computing averages in a decentralized way. Namely, we will show that
a number of distributed control and signal processing problems can be solved
straightforwardly if solutions to the averaging problem are available. The rest
of the thesis will be concerned with algorithms for the averaging problem and
its generalizations. We will (i) derive the fastest known averaging algorithms
in a variety of settings and subject to a variety of communication and storage
constraints (ii) prove a lower bound identifying a fundamental barrier for
averaging algorithms (iii) propose a new model for distributed function
computation which reflects the constraints facing many large-scale networks,
and nearly characterize the general class of functions which can be computed in
this model.Comment: Ph.D. thesis, Department of Electrical Engineering and Computer
Science, MIT, September 201
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Information dissemination via random walks
Information dissemination is a fundamental task in distributed computing:
How to deliver a piece of information from a node of a network to some or all other nodes?
In the face of large and still growing modern networks, it is imperative that dissemination algorithms are decentralised and can operate under unreliable conditions.
In the past decades, randomised rumour spreading algorithms
have addressed these challenges.
In these algorithms, a message is initially placed at a source node of a network, and, at regular intervals, each node contacts a randomly selected neighbour.
A message may be transmitted in one or both directions during each of these communications, depending on the exact protocol.
The main measure of performance for these algorithms is their broadcast time, which is the time until a message originating from a source node is disseminated to all nodes of the network.
Apart from being extremely simple and robust to failures, randomised rumour spreading achieves theoretically optimal broadcast time in many common network topologies.
In this thesis, we propose an agent-based information dissemination algorithm, called Visit-Exchange.
In our protocol, a number of agents perform independent random walks in the network.
An agent becomes informed when it visits a node that has a message, and later informs all future nodes it visits.
Visit-Exchange shares many of the properties of randomised rumour spreading, namely, it is very simple and uses the same amount of communication in a unit of time.
Moreover, the protocol can be used as a simple model of non-recoverable epidemic processes.
We investigate the broadcast time of Visit-Exchange on a variety of network topologies, and compare it to traditional rumour spreading.
On dense regular networks we show that the two types of protocols are equivalent, which means that in this setting the vast literature on randomised rumour spreading applies in our model as well.
Since many networks of interest, including real-world ones, are very sparse, we also study agent-based broadcast for sparse networks.
Our results include almost optimal or optimal bounds for sparse regular graphs, expanders, random regular graphs, balanced trees and grids.
We establish that depending on the network topology, Visit-Exchange may be either slower or faster than traditional rumour spreading.
In particular, in graphs consisting of hubs that are not well connected, broadcast using agents can be significantly faster.
Our conclusion is that a combined broadcasting protocol that simultaneously uses both traditional rumour spreading and agent-based dissemination can be fast on a larger range of topologies than each of its components separately.Gates Cambridge Trust, St John's College Benefactors' Scholarshi
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