12,335 research outputs found
A Coding Theoretic Approach for Evaluating Accumulate Distribution on Minimum Cut Capacity of Weighted Random Graphs
The multicast capacity of a directed network is closely related to the
- maximum flow, which is equal to the - minimum cut capacity due to
the max-flow min-cut theorem. If the topology of a network (or link capacities)
is dynamically changing or have stochastic nature, it is not so trivial to
predict statistical properties on the maximum flow. In this paper, we present a
coding theoretic approach for evaluating the accumulate distribution of the
minimum cut capacity of weighted random graphs. The main feature of our
approach is to utilize the correspondence between the cut space of a graph and
a binary LDGM (low-density generator-matrix) code with column weight 2. The
graph ensemble treated in the paper is a weighted version of
Erd\H{o}s-R\'{e}nyi random graph ensemble. The main contribution of our work is
a combinatorial lower bound for the accumulate distribution of the minimum cut
capacity. From some computer experiments, it is observed that the lower bound
derived here reflects the actual statistical behavior of the minimum cut
capacity.Comment: 5 pages, 2 figures, submitted to IEEE ISIT 201
k-connectivity of Random Graphs and Random Geometric Graphs in Node Fault Model
k-connectivity of random graphs is a fundamental property indicating
reliability of multi-hop wireless sensor networks (WSN). WSNs comprising of
sensor nodes with limited power resources are modeled by random graphs with
unreliable nodes, which is known as the node fault model. In this paper, we
investigate k-connectivity of random graphs in the node fault model by
evaluating the network breakdown probability, i.e., the disconnectivity
probability of random graphs after stochastic node removals. Using the notion
of a strongly typical set, we obtain universal asymptotic upper and lower
bounds of the network breakdown probability. The bounds are applicable both to
random graphs and to random geometric graphs. We then consider three
representative random graph ensembles: the Erdos-Renyi random graph as the
simplest case, the random intersection graph for WSNs with random key
predistribution schemes, and the random geometric graph as a model of WSNs
generated by random sensor node deployment. The bounds unveil the existence of
the phase transition of the network breakdown probability for those ensembles.Comment: 6 page
Link Prediction in Complex Networks: A Survey
Link prediction in complex networks has attracted increasing attention from
both physical and computer science communities. The algorithms can be used to
extract missing information, identify spurious interactions, evaluate network
evolving mechanisms, and so on. This article summaries recent progress about
link prediction algorithms, emphasizing on the contributions from physical
perspectives and approaches, such as the random-walk-based methods and the
maximum likelihood methods. We also introduce three typical applications:
reconstruction of networks, evaluation of network evolving mechanism and
classification of partially labelled networks. Finally, we introduce some
applications and outline future challenges of link prediction algorithms.Comment: 44 pages, 5 figure
Organic Design of Massively Distributed Systems: A Complex Networks Perspective
The vision of Organic Computing addresses challenges that arise in the design
of future information systems that are comprised of numerous, heterogeneous,
resource-constrained and error-prone components or devices. Here, the notion
organic particularly highlights the idea that, in order to be manageable, such
systems should exhibit self-organization, self-adaptation and self-healing
characteristics similar to those of biological systems. In recent years, the
principles underlying many of the interesting characteristics of natural
systems have been investigated from the perspective of complex systems science,
particularly using the conceptual framework of statistical physics and
statistical mechanics. In this article, we review some of the interesting
relations between statistical physics and networked systems and discuss
applications in the engineering of organic networked computing systems with
predictable, quantifiable and controllable self-* properties.Comment: 17 pages, 14 figures, preprint of submission to Informatik-Spektrum
published by Springe
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