25,165 research outputs found
Connectivity measures for internet topologies.
The topology of the Internet has initially been modelled as an undirected graph, where vertices correspond to so-called Autonomous Systems (ASs),and edges correspond to physical links between pairs of ASs. However, in order to capture the impact of routing policies, it has recently become apparent that one needs to classify the edges according to the existing economic relationships (customer-provider, peer-to-peer or siblings) between the ASs. This leads to a directed graph model in which traffic can be sent only along so-called valley-free paths. Four different algorithms have been proposed in the literature for inferring AS relationships using publicly available data from routing tables. We investigate the differences in the graph models produced by these algorithms, focussing on connectivity measures. To this aim, we compute the maximum number of vertex-disjoint valley-free paths between ASs as well as the size of a minimum cut separating a pair of ASs. Although these problems are solvable in polynomial time for ordinary graphs, they are NP-hard in our setting. We formulate the two problems as integer programs, and we propose a number of exact algorithms for solving them. For the problem of finding the maximum number of vertex-disjoint paths, we discuss two algorithms; the first one is a branch-and-price algorithm based on the IP formulation, and the second algorithm is a non LP based branch-and-bound algorithm. For the problem of finding minimum cuts we use a branch-and-cut algo rithm, based on the IP formulation of this problem. Using these algorithms, we obtain exact solutions for both problems in reasonable time. It turns out that there is a large gap in terms of the connectivity measures between the undirected and directed models. This finding supports our conclusion that economic relationships need to be taken into account when building a topology of the Internet.Research; Internet;
Fundamentals of Large Sensor Networks: Connectivity, Capacity, Clocks and Computation
Sensor networks potentially feature large numbers of nodes that can sense
their environment over time, communicate with each other over a wireless
network, and process information. They differ from data networks in that the
network as a whole may be designed for a specific application. We study the
theoretical foundations of such large scale sensor networks, addressing four
fundamental issues- connectivity, capacity, clocks and function computation.
To begin with, a sensor network must be connected so that information can
indeed be exchanged between nodes. The connectivity graph of an ad-hoc network
is modeled as a random graph and the critical range for asymptotic connectivity
is determined, as well as the critical number of neighbors that a node needs to
connect to. Next, given connectivity, we address the issue of how much data can
be transported over the sensor network. We present fundamental bounds on
capacity under several models, as well as architectural implications for how
wireless communication should be organized.
Temporal information is important both for the applications of sensor
networks as well as their operation.We present fundamental bounds on the
synchronizability of clocks in networks, and also present and analyze
algorithms for clock synchronization. Finally we turn to the issue of gathering
relevant information, that sensor networks are designed to do. One needs to
study optimal strategies for in-network aggregation of data, in order to
reliably compute a composite function of sensor measurements, as well as the
complexity of doing so. We address the issue of how such computation can be
performed efficiently in a sensor network and the algorithms for doing so, for
some classes of functions.Comment: 10 pages, 3 figures, Submitted to the Proceedings of the IEE
Complex networks analysis in socioeconomic models
This chapter aims at reviewing complex networks models and methods that were
either developed for or applied to socioeconomic issues, and pertinent to the
theme of New Economic Geography. After an introduction to the foundations of
the field of complex networks, the present summary adds insights on the
statistical mechanical approach, and on the most relevant computational aspects
for the treatment of these systems. As the most frequently used model for
interacting agent-based systems, a brief description of the statistical
mechanics of the classical Ising model on regular lattices, together with
recent extensions of the same model on small-world Watts-Strogatz and
scale-free Albert-Barabasi complex networks is included. Other sections of the
chapter are devoted to applications of complex networks to economics, finance,
spreading of innovations, and regional trade and developments. The chapter also
reviews results involving applications of complex networks to other relevant
socioeconomic issues, including results for opinion and citation networks.
Finally, some avenues for future research are introduced before summarizing the
main conclusions of the chapter.Comment: 39 pages, 185 references, (not final version of) a chapter prepared
for Complexity and Geographical Economics - Topics and Tools, P.
Commendatore, S.S. Kayam and I. Kubin Eds. (Springer, to be published
Approximate Consensus in Highly Dynamic Networks: The Role of Averaging Algorithms
In this paper, we investigate the approximate consensus problem in highly
dynamic networks in which topology may change continually and unpredictably. We
prove that in both synchronous and partially synchronous systems, approximate
consensus is solvable if and only if the communication graph in each round has
a rooted spanning tree, i.e., there is a coordinator at each time. The striking
point in this result is that the coordinator is not required to be unique and
can change arbitrarily from round to round. Interestingly, the class of
averaging algorithms, which are memoryless and require no process identifiers,
entirely captures the solvability issue of approximate consensus in that the
problem is solvable if and only if it can be solved using any averaging
algorithm. Concerning the time complexity of averaging algorithms, we show that
approximate consensus can be achieved with precision of in a
coordinated network model in synchronous
rounds, and in rounds when
the maximum round delay for a message to be delivered is . While in
general, an upper bound on the time complexity of averaging algorithms has to
be exponential, we investigate various network models in which this exponential
bound in the number of nodes reduces to a polynomial bound. We apply our
results to networked systems with a fixed topology and classical benign fault
models, and deduce both known and new results for approximate consensus in
these systems. In particular, we show that for solving approximate consensus, a
complete network can tolerate up to 2n-3 arbitrarily located link faults at
every round, in contrast with the impossibility result established by Santoro
and Widmayer (STACS '89) showing that exact consensus is not solvable with n-1
link faults per round originating from the same node
On directed information theory and Granger causality graphs
Directed information theory deals with communication channels with feedback.
When applied to networks, a natural extension based on causal conditioning is
needed. We show here that measures built from directed information theory in
networks can be used to assess Granger causality graphs of stochastic
processes. We show that directed information theory includes measures such as
the transfer entropy, and that it is the adequate information theoretic
framework needed for neuroscience applications, such as connectivity inference
problems.Comment: accepted for publications, Journal of Computational Neuroscienc
Graph analysis of functional brain networks: practical issues in translational neuroscience
The brain can be regarded as a network: a connected system where nodes, or
units, represent different specialized regions and links, or connections,
represent communication pathways. From a functional perspective communication
is coded by temporal dependence between the activities of different brain
areas. In the last decade, the abstract representation of the brain as a graph
has allowed to visualize functional brain networks and describe their
non-trivial topological properties in a compact and objective way. Nowadays,
the use of graph analysis in translational neuroscience has become essential to
quantify brain dysfunctions in terms of aberrant reconfiguration of functional
brain networks. Despite its evident impact, graph analysis of functional brain
networks is not a simple toolbox that can be blindly applied to brain signals.
On the one hand, it requires a know-how of all the methodological steps of the
processing pipeline that manipulates the input brain signals and extract the
functional network properties. On the other hand, a knowledge of the neural
phenomenon under study is required to perform physiological-relevant analysis.
The aim of this review is to provide practical indications to make sense of
brain network analysis and contrast counterproductive attitudes
Synchronization in complex networks
Synchronization processes in populations of locally interacting elements are
in the focus of intense research in physical, biological, chemical,
technological and social systems. The many efforts devoted to understand
synchronization phenomena in natural systems take now advantage of the recent
theory of complex networks. In this review, we report the advances in the
comprehension of synchronization phenomena when oscillating elements are
constrained to interact in a complex network topology. We also overview the new
emergent features coming out from the interplay between the structure and the
function of the underlying pattern of connections. Extensive numerical work as
well as analytical approaches to the problem are presented. Finally, we review
several applications of synchronization in complex networks to different
disciplines: biological systems and neuroscience, engineering and computer
science, and economy and social sciences.Comment: Final version published in Physics Reports. More information
available at http://synchronets.googlepages.com
A Bag-of-Paths Node Criticality Measure
This work compares several node (and network) criticality measures
quantifying to which extend each node is critical with respect to the
communication flow between nodes of the network, and introduces a new measure
based on the Bag-of-Paths (BoP) framework. Network disconnection simulation
experiments show that the new BoP measure outperforms all the other measures on
a sample of Erdos-Renyi and Albert-Barabasi graphs. Furthermore, a faster
(still O(n^3)), approximate, BoP criticality relying on the Sherman-Morrison
rank-one update of a matrix is introduced for tackling larger networks. This
approximate measure shows similar performances as the original, exact, one
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