42,998 research outputs found
Systematic Topology Analysis and Generation Using Degree Correlations
We present a new, systematic approach for analyzing network topologies. We
first introduce the dK-series of probability distributions specifying all
degree correlations within d-sized subgraphs of a given graph G. Increasing
values of d capture progressively more properties of G at the cost of more
complex representation of the probability distribution. Using this series, we
can quantitatively measure the distance between two graphs and construct random
graphs that accurately reproduce virtually all metrics proposed in the
literature. The nature of the dK-series implies that it will also capture any
future metrics that may be proposed. Using our approach, we construct graphs
for d=0,1,2,3 and demonstrate that these graphs reproduce, with increasing
accuracy, important properties of measured and modeled Internet topologies. We
find that the d=2 case is sufficient for most practical purposes, while d=3
essentially reconstructs the Internet AS- and router-level topologies exactly.
We hope that a systematic method to analyze and synthesize topologies offers a
significant improvement to the set of tools available to network topology and
protocol researchers.Comment: Final versio
Generating realistic scaled complex networks
Research on generative models is a central project in the emerging field of
network science, and it studies how statistical patterns found in real networks
could be generated by formal rules. Output from these generative models is then
the basis for designing and evaluating computational methods on networks, and
for verification and simulation studies. During the last two decades, a variety
of models has been proposed with an ultimate goal of achieving comprehensive
realism for the generated networks. In this study, we (a) introduce a new
generator, termed ReCoN; (b) explore how ReCoN and some existing models can be
fitted to an original network to produce a structurally similar replica, (c)
use ReCoN to produce networks much larger than the original exemplar, and
finally (d) discuss open problems and promising research directions. In a
comparative experimental study, we find that ReCoN is often superior to many
other state-of-the-art network generation methods. We argue that ReCoN is a
scalable and effective tool for modeling a given network while preserving
important properties at both micro- and macroscopic scales, and for scaling the
exemplar data by orders of magnitude in size.Comment: 26 pages, 13 figures, extended version, a preliminary version of the
paper was presented at the 5th International Workshop on Complex Networks and
their Application
An efficient memetic, permutation-based evolutionary algorithm for real-world train timetabling
Train timetabling is a difficult and very tightly constrained combinatorial
problem that deals with the construction of train schedules. We focus on the
particular problem of local reconstruction of the schedule following a small
perturbation, seeking minimisation of the total accumulated delay by adapting
times of departure and arrival for each train and allocation of resources
(tracks, routing nodes, etc.). We describe a permutation-based evolutionary
algorithm that relies on a semi-greedy heuristic to gradually reconstruct the
schedule by inserting trains one after the other following the permutation.
This algorithm can be hybridised with ILOG commercial MIP programming tool
CPLEX in a coarse-grained manner: the evolutionary part is used to quickly
obtain a good but suboptimal solution and this intermediate solution is refined
using CPLEX. Experimental results are presented on a large real-world case
involving more than one million variables and 2 million constraints. Results
are surprisingly good as the evolutionary algorithm, alone or hybridised,
produces excellent solutions much faster than CPLEX alone
Reduced-Dimension Linear Transform Coding of Correlated Signals in Networks
A model, called the linear transform network (LTN), is proposed to analyze
the compression and estimation of correlated signals transmitted over directed
acyclic graphs (DAGs). An LTN is a DAG network with multiple source and
receiver nodes. Source nodes transmit subspace projections of random correlated
signals by applying reduced-dimension linear transforms. The subspace
projections are linearly processed by multiple relays and routed to intended
receivers. Each receiver applies a linear estimator to approximate a subset of
the sources with minimum mean squared error (MSE) distortion. The model is
extended to include noisy networks with power constraints on transmitters. A
key task is to compute all local compression matrices and linear estimators in
the network to minimize end-to-end distortion. The non-convex problem is solved
iteratively within an optimization framework using constrained quadratic
programs (QPs). The proposed algorithm recovers as special cases the regular
and distributed Karhunen-Loeve transforms (KLTs). Cut-set lower bounds on the
distortion region of multi-source, multi-receiver networks are given for linear
coding based on convex relaxations. Cut-set lower bounds are also given for any
coding strategy based on information theory. The distortion region and
compression-estimation tradeoffs are illustrated for different communication
demands (e.g. multiple unicast), and graph structures.Comment: 33 pages, 7 figures, To appear in IEEE Transactions on Signal
Processin
Detecting early signs of the 2007-2008 crisis in the world trade
Since 2007, several contributions have tried to identify early-warning
signals of the financial crisis. However, the vast majority of analyses has
focused on financial systems and little theoretical work has been done on the
economic counterpart. In the present paper we fill this gap and employ the
theoretical tools of network theory to shed light on the response of world
trade to the financial crisis of 2007 and the economic recession of 2008-2009.
We have explored the evolution of the bipartite World Trade Web (WTW) across
the years 1995-2010, monitoring the behavior of the system both before and
after 2007. Our analysis shows early structural changes in the WTW topology:
since 2003, the WTW becomes increasingly compatible with the picture of a
network where correlations between countries and products are progressively
lost. Moreover, the WTW structural modification can be considered as concluded
in 2010, after a seemingly stationary phase of three years. We have also
refined our analysis by considering specific subsets of countries and products:
the most statistically significant early-warning signals are provided by the
most volatile macrosectors, especially when measured on developing countries,
suggesting the emerging economies as being the most sensitive ones to the
global economic cycles.Comment: 18 pages, 9 figure
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