200,722 research outputs found
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
Differential Privacy from Locally Adjustable Graph Algorithms: -Core Decomposition, Low Out-Degree Ordering, and Densest Subgraphs
Differentially private algorithms allow large-scale data analytics while
preserving user privacy. Designing such algorithms for graph data is gaining
importance with the growth of large networks that model various (sensitive)
relationships between individuals. While there exists a rich history of
important literature in this space, to the best of our knowledge, no results
formalize a relationship between certain parallel and distributed graph
algorithms and differentially private graph analysis. In this paper, we define
\emph{locally adjustable} graph algorithms and show that algorithms of this
type can be transformed into differentially private algorithms.
Our formalization is motivated by a set of results that we present in the
central and local models of differential privacy for a number of problems,
including -core decomposition, low out-degree ordering, and densest
subgraphs. First, we design an -edge differentially private (DP)
algorithm that returns a subset of nodes that induce a subgraph of density at
least
where is the density of the densest subgraph in the input graph (for any
constant ). This algorithm achieves a two-fold improvement on the
multiplicative approximation factor of the previously best-known private
densest subgraph algorithms while maintaining a near-linear runtime.
Then, we present an -locally edge differentially private (LEDP)
algorithm for -core decompositions. Our LEDP algorithm provides approximates
the core numbers (for any constant ) with multiplicative
and additive error.
This is the first differentially private algorithm that outputs private
-core decomposition statistics
A distributed, compact routing protocol for the Internet
The Internet has grown in size at rapid rates since BGP records began, and continues to do so. This has raised concerns about the scalability of the current BGP routing system, as the routing state at each router in a shortest-path routing protocol will grow at a supra-linearly rate as the network grows. The concerns are that the memory capacity of routers will not be able to keep up with demands, and that the growth of the Internet will become ever more cramped as more and more of the world seeks the benefits of being connected.
Compact routing schemes, where the routing state grows only sub-linearly relative to the growth of the network, could solve this problem and ensure that router memory would not be a bottleneck to Internet growth. These schemes trade away shortest-path routing for scalable memory state, by allowing some paths to have a certain amount of bounded “stretch”.
The most promising such scheme is Cowen Routing, which can provide scalable, compact routing state for Internet routing, while still providing shortest-path routing to nearly all other nodes, with only slightly stretched paths to a very small subset of the network. Currently, there is no fully distributed form of Cowen Routing that would be practical for the Internet.
This dissertation describes a fully distributed and compact protocol for Cowen routing, using the k-core graph decomposition.
Previous compact routing work showed the k-core graph decomposition is useful for Cowen Routing on the Internet, but no distributed form existed. This dissertation gives a distributed k-core algorithm optimised to be efficient on dynamic graphs, along with with proofs of its correctness. The performance and efficiency of this distributed k-core algorithm is evaluated on large, Internet AS graphs, with excellent results.
This dissertation then goes on to describe a fully distributed and compact Cowen Routing protocol. This protocol being comprised of a landmark selection process for Cowen Routing using the k-core algorithm, with mechanisms to ensure compact state at all times, including at bootstrap; a local cluster routing process, with mechanisms for policy application and control of cluster sizes, ensuring again that state can remain compact at all times; and a landmark routing process is described with a prioritisation mechanism for announcements that ensures compact state at all times
Shared-memory Graph Truss Decomposition
We present PKT, a new shared-memory parallel algorithm and OpenMP
implementation for the truss decomposition of large sparse graphs. A k-truss is
a dense subgraph definition that can be considered a relaxation of a clique.
Truss decomposition refers to a partitioning of all the edges in the graph
based on their k-truss membership. The truss decomposition of a graph has many
applications. We show that our new approach PKT consistently outperforms other
truss decomposition approaches for a collection of large sparse graphs and on a
24-core shared-memory server. PKT is based on a recently proposed algorithm for
k-core decomposition.Comment: 10 pages, conference submissio
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