Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
On power-law relationships of the Internet topology
Proceedings of the conference on Applications, technologies, architectures, and protocols for computer communication
Greedily finding a dense subgraph
Journal of Algorithms
On the marginal utility of network topology measurements
IMW '01 Proceedings of the 1st ACM SIGCOMM Workshop on Internet Measurement
Approximation algorithms for maximization problems arising in graph partitioning
Journal of Algorithms
Network topology generators: degree-based vs. structural
Proceedings of the 2002 conference on Applications, technologies, architectures, and protocols for computer communications
On the densest k-subgraph problems
On the densest k-subgraph problems
On the power-law random graph model of massive data networks
Performance Evaluation - Internet performance symposium (IPS 2002)
A New Conceptual Clustering Framework
Machine Learning
DIMES: let the internet measure itself
ACM SIGCOMM Computer Communication Review
A geographic directed preferential internet topology model
Computer Networks: The International Journal of Computer and Telecommunications Networking
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The connectivity of the Internet crucially depends on the relationships between thousands of Autonomous Systems (ASes) that exchange routing information using the Border Gateway Protocol (BGP). These relationships can be modeled as a graph, called the AS-graph, in which the vertices model the ASes, and the edges model the peering arrangements between the ASes. Based on topological studies, it is widely believed that the Internet graph contains a central dense-core: Informally, this is a small set of high-degree, tightly interconnected ASes that participate in a large fraction of end-to-end routes. Finding this dense-core is a very important practical task when analyzing the Internet's topology. In this work we introduce a randomized sublinear algorithm that finds a dense-core of the AS-graph. We mathematically prove the correctness of our algorithm, bound the density of the core it returns, and analyze its running time. We also implemented our algorithm and tested it on real AS-graph data and on real undirected version of WWW network data. Our results show that the core discovered by our algorithm is nearly identical to the cores found by existing algorithms - at a fraction of the running time.