11,962 research outputs found
Understanding edge-connectivity in the Internet through core-decomposition
Internet is a complex network composed by several networks: the Autonomous
Systems, each one designed to transport information efficiently. Routing
protocols aim to find paths between nodes whenever it is possible (i.e., the
network is not partitioned), or to find paths verifying specific constraints
(e.g., a certain QoS is required). As connectivity is a measure related to both
of them (partitions and selected paths) this work provides a formal lower bound
to it based on core-decomposition, under certain conditions, and low complexity
algorithms to find it. We apply them to analyze maps obtained from the
prominent Internet mapping projects, using the LaNet-vi open-source software
for its visualization
K-core decomposition of Internet graphs: hierarchies, self-similarity and measurement biases
We consider the -core decomposition of network models and Internet graphs
at the autonomous system (AS) level. The -core analysis allows to
characterize networks beyond the degree distribution and uncover structural
properties and hierarchies due to the specific architecture of the system. We
compare the -core structure obtained for AS graphs with those of several
network models and discuss the differences and similarities with the real
Internet architecture. The presence of biases and the incompleteness of the
real maps are discussed and their effect on the -core analysis is assessed
with numerical experiments simulating biased exploration on a wide range of
network models. We find that the -core analysis provides an interesting
characterization of the fluctuations and incompleteness of maps as well as
information helping to discriminate the original underlying structure
Mathematics and the Internet: A Source of Enormous Confusion and Great Potential
Graph theory models the Internet mathematically, and a number of plausible mathematically intersecting network models for the Internet have been developed and studied. Simultaneously, Internet researchers have developed methodology to use real data to validate, or invalidate, proposed Internet models. The authors look at these parallel developments, particularly as they apply to scale-free network models of the preferential attachment type
VoG: Summarizing and Understanding Large Graphs
How can we succinctly describe a million-node graph with a few simple
sentences? How can we measure the "importance" of a set of discovered subgraphs
in a large graph? These are exactly the problems we focus on. Our main ideas
are to construct a "vocabulary" of subgraph-types that often occur in real
graphs (e.g., stars, cliques, chains), and from a set of subgraphs, find the
most succinct description of a graph in terms of this vocabulary. We measure
success in a well-founded way by means of the Minimum Description Length (MDL)
principle: a subgraph is included in the summary if it decreases the total
description length of the graph.
Our contributions are three-fold: (a) formulation: we provide a principled
encoding scheme to choose vocabulary subgraphs; (b) algorithm: we develop
\method, an efficient method to minimize the description cost, and (c)
applicability: we report experimental results on multi-million-edge real
graphs, including Flickr and the Notre Dame web graph.Comment: SIAM International Conference on Data Mining (SDM) 201
{VoG}: {Summarizing} and Understanding Large Graphs
How can we succinctly describe a million-node graph with a few simple sentences? How can we measure the "importance" of a set of discovered subgraphs in a large graph? These are exactly the problems we focus on. Our main ideas are to construct a "vocabulary" of subgraph-types that often occur in real graphs (e.g., stars, cliques, chains), and from a set of subgraphs, find the most succinct description of a graph in terms of this vocabulary. We measure success in a well-founded way by means of the Minimum Description Length (MDL) principle: a subgraph is included in the summary if it decreases the total description length of the graph. Our contributions are three-fold: (a) formulation: we provide a principled encoding scheme to choose vocabulary subgraphs; (b) algorithm: we develop \method, an efficient method to minimize the description cost, and (c) applicability: we report experimental results on multi-million-edge real graphs, including Flickr and the Notre Dame web graph
Opportunistic Third-Party Backhaul for Cellular Wireless Networks
With high capacity air interfaces and large numbers of small cells, backhaul
-- the wired connectivity to base stations -- is increasingly becoming the cost
driver in cellular wireless networks. One reason for the high cost of backhaul
is that capacity is often purchased on leased lines with guaranteed rates
provisioned to peak loads. In this paper, we present an alternate
\emph{opportunistic backhaul} model where third parties provide base stations
and backhaul connections and lease out excess capacity in their networks to the
cellular provider when available, presumably at significantly lower costs than
guaranteed connections. We describe a scalable architecture for such
deployments using open access femtocells, which are small plug-and-play base
stations that operate in the carrier's spectrum but can connect directly into
the third party provider's wired network. Within the proposed architecture, we
present a general user association optimization algorithm that enables the
cellular provider to dynamically determine which mobiles should be assigned to
the third-party femtocells based on the traffic demands, interference and
channel conditions and third-party access pricing. Although the optimization is
non-convex, the algorithm uses a computationally efficient method for finding
approximate solutions via dual decomposition. Simulations of the deployment
model based on actual base station locations are presented that show that large
capacity gains are achievable if adoption of third-party, open access
femtocells can reach even a small fraction of the current market penetration of
WiFi access points.Comment: 9 pages, 6 figure
MEDUSA - New Model of Internet Topology Using k-shell Decomposition
The k-shell decomposition of a random graph provides a different and more
insightful separation of the roles of the different nodes in such a graph than
does the usual analysis in terms of node degrees. We develop this approach in
order to analyze the Internet's structure at a coarse level, that of the
"Autonomous Systems" or ASes, the subnetworks out of which the Internet is
assembled. We employ new data from DIMES (see http://www.netdimes.org), a
distributed agent-based mapping effort which at present has attracted over 3800
volunteers running more than 7300 DIMES clients in over 85 countries. We
combine this data with the AS graph information available from the RouteViews
project at Univ. Oregon, and have obtained an Internet map with far more detail
than any previous effort.
The data suggests a new picture of the AS-graph structure, which
distinguishes a relatively large, redundantly connected core of nearly 100 ASes
and two components that flow data in and out from this core. One component is
fractally interconnected through peer links; the second makes direct
connections to the core only. The model which results has superficial
similarities with and important differences from the "Jellyfish" structure
proposed by Tauro et al., so we call it a "Medusa." We plan to use this picture
as a framework for measuring and extrapolating changes in the Internet's
physical structure. Our k-shell analysis may also be relevant for estimating
the function of nodes in the "scale-free" graphs extracted from other
naturally-occurring processes.Comment: 24 pages, 17 figure
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