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256
Measuring ISP Topologies with Rocketfuel
 In Proc. ACM SIGCOMM
, 2002
"... To date, realistic ISP topologies have not been accessible to the research community, leaving work that depends on topology on an uncertain footing. In this paper, we present new Internet mapping techniques that have enabled us to directly measure routerlevel ISP topologies. Our techniques reduce t ..."
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Cited by 843 (28 self)
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To date, realistic ISP topologies have not been accessible to the research community, leaving work that depends on topology on an uncertain footing. In this paper, we present new Internet mapping techniques that have enabled us to directly measure routerlevel ISP topologies. Our techniques reduce the number of required traces compared to a bruteforce, alltoall approach by three orders of magnitude without a significant loss in accuracy. They include the use of BGP routing tables to focus the measurements, exploiting properties of IP routing to eliminate redundant measurements, better alias resolution, and the use of DNS to divide each map into POPs and backbone. We collect maps from ten diverse ISPs using our techniques, and find that our maps are substantially more complete than those of earlier Internet mapping efforts. We also report on properties of these maps, including the size of POPs, distribution of router outdegree, and the interdomain peering structure. As part of this work, we release our maps to the community.
RMAT: A recursive model for graph mining
 In Fourth SIAM International Conference on Data Mining (SDM’ 04
, 2004
"... How does a ‘normal ’ computer (or social) network look like? How can we spot ‘abnormal ’ subnetworks in the Internet, or web graph? The answer to such questions is vital for outlier detection (terrorist networks, or illegal moneylaundering rings), forecasting, and simulations (“how will a computer ..."
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Cited by 245 (17 self)
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How does a ‘normal ’ computer (or social) network look like? How can we spot ‘abnormal ’ subnetworks in the Internet, or web graph? The answer to such questions is vital for outlier detection (terrorist networks, or illegal moneylaundering rings), forecasting, and simulations (“how will a computer virus spread?”). The heart of the problem is finding the properties of real graphs that seem to persist over multiple disciplines. We list such “laws ” and, more importantly, we propose a simple, parsimonious model, the “recursive matrix ” (RMAT) model, which can quickly generate realistic graphs, capturing the essence of each graph in only a few parameters. Contrary to existing generators, our model can trivially generate weighted, directed and bipartite graphs; it subsumes the celebrated ErdősRényi model as a special case; it can match the power law behaviors, as well as the deviations from them (like the “winner does not take it all ” model of Pennock et al. [21]). We present results on multiple, large real graphs, where we show that our parameter fitting algorithm (AutoMATfast) fits them very well. 1
Random Walks in PeertoPeer Networks
, 2004
"... We quantify the effectiveness of random walks for searching and construction of unstructured peertopeer (P2P) networks. For searching, we argue that random walks achieve improvement over flooding in the case of clustered overlay topologies and in the case of reissuing the same request several tim ..."
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Cited by 226 (3 self)
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We quantify the effectiveness of random walks for searching and construction of unstructured peertopeer (P2P) networks. For searching, we argue that random walks achieve improvement over flooding in the case of clustered overlay topologies and in the case of reissuing the same request several times. For construction, we argue that an expander can be maintained dynamically with constant operations per addition. The key technical ingredient of our approach is a deep result of stochastic processes indicating that samples taken from consecutive steps of a random walk can achieve statistical properties similar to independent sampling (if the second eigenvalue of the transition matrix is bounded away from 1, which translates to good expansion of the network; such connectivity is desired, and believed to hold, in every reasonable network and network model). This property has been previously used in complexity theory for construction of pseudorandom number generators. We reveal another facet of this theory and translate savings in random bits to savings in processing overhead.
A FirstPrinciples Approach to Understanding the Internet's Routerlevel Topology
, 2004
"... A detailed understanding of the many facets of the Internet's topological structure is critical for evaluating the performance of networking protocols, for assessing the effectiveness of proposed techniques to protect the network from nefarious intrusions and attacks, or for developing improved ..."
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Cited by 213 (19 self)
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A detailed understanding of the many facets of the Internet's topological structure is critical for evaluating the performance of networking protocols, for assessing the effectiveness of proposed techniques to protect the network from nefarious intrusions and attacks, or for developing improved designs for resource provisioning. Previous studies of topology have focused on interpreting measurements or on phenomenological descriptions and evaluation of graphtheoretic properties of topology generators. We propose a complementary approach of combining a more subtle use of statistics and graph theory with a firstprinciples theory of routerlevel topology that reflects practical constraints and tradeoffs. While there is an inevitable tradeoff between model complexity and fidelity, a challenge is to distill from the seemingly endless list of potentially relevant technological and economic issues the features that are most essential to a solid understanding of the intrinsic fundamentals of network topology. We claim that very simple models that incorporate hard technological constraints on router and link bandwidth and connectivity, together with abstract models of user demand and network performance, can successfully address this challenge and further resolve much of the confusion and controversy that has surrounded topology generation and evaluation.
Network Topology Generators: DegreeBased vs. Structural
, 2002
"... Following the longheld belief that the Internet is hierarchical, the network topology generators most widely used by the Internet research community, TransitStub and Tiers, create networks with a deliberately hierarchical structure. However, in 1999 a seminal paper by Faloutsos et al. revealed tha ..."
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Cited by 207 (17 self)
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Following the longheld belief that the Internet is hierarchical, the network topology generators most widely used by the Internet research community, TransitStub and Tiers, create networks with a deliberately hierarchical structure. However, in 1999 a seminal paper by Faloutsos et al. revealed that the Internet's degree distribution is a powerlaw. Because the degree distributions produced by the TransitStub and Tiers generators are not powerlaws, the research community has largely dismissed them as inadequate and proposed new network generators that attempt to generate graphs with powerlaw degree distributions.
Quantifying the causes of path inflation.
 In SIGCOMM,
, 2003
"... ABSTRACT Researchers have shown that the Internet exhibits path inflationendtoend paths can be significantly longer than necessary. We present a tracedriven study of 65 ISPs that characterizes the root causes of path inflation, namely topology and routing policy choices within an ISP, between pa ..."
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Cited by 138 (26 self)
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ABSTRACT Researchers have shown that the Internet exhibits path inflationendtoend paths can be significantly longer than necessary. We present a tracedriven study of 65 ISPs that characterizes the root causes of path inflation, namely topology and routing policy choices within an ISP, between pairs of ISPs, and across the global Internet. To do so, we develop and validate novel techniques to infer intradomain and peering policies from endtoend measurements. We provide the first measured characterization of ISP peering policies. In addition to "earlyexit," we observe a significant degree of helpful nonearlyexit, loadbalancing, and other policies in use between peers. We find that traffic engineering (the explicit addition of policy constraints on top of topology constraints) is widespread in both intraand interdomain routing. However, intradomain traffic engineering has minimal impact on path inflation, while peering policies and interdomain routing lead to significant inflation. We argue that the underlying cause of interdomain path inflation is the lack of BGP policy controls to provide convenient engineering of good paths across ISPs.
Graph mining: laws, generators, and algorithms
 ACM COMPUT SURV (CSUR
, 2006
"... How does the Web look? How could we tell an abnormal social network from a normal one? These and similar questions are important in many fields where the data can intuitively be cast as a graph; examples range from computer networks to sociology to biology and many more. Indeed, any M: N relation in ..."
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Cited by 132 (7 self)
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How does the Web look? How could we tell an abnormal social network from a normal one? These and similar questions are important in many fields where the data can intuitively be cast as a graph; examples range from computer networks to sociology to biology and many more. Indeed, any M: N relation in database terminology can be represented as a graph. A lot of these questions boil down to the following: “How can we generate synthetic but realistic graphs? ” To answer this, we must first understand what patterns are common in realworld graphs and can thus be considered a mark of normality/realism. This survey give an overview of the incredible variety of work that has been done on these problems. One of our main contributions is the integration of points of view from physics, mathematics, sociology, and computer science. Further, we briefly describe recent advances on some related and interesting graph problems.
GraphTheoretic Analysis of Structured PeertoPeer Systems: Routing Distances and Fault Resilience
, 2003
"... This paper examines graphtheoretic properties of existing peertopeer architectures and proposes a new infrastructure based on optimaldiameter de Bruijn graphs. Since generalized de Bruijn graphs possess very short average routing distances and high resilience to node failure, they are well suite ..."
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Cited by 127 (7 self)
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This paper examines graphtheoretic properties of existing peertopeer architectures and proposes a new infrastructure based on optimaldiameter de Bruijn graphs. Since generalized de Bruijn graphs possess very short average routing distances and high resilience to node failure, they are well suited for structured peertopeer networks. Using the example of Chord, CAN, and de Bruijn, we first study routing performance, graph expansion, and clustering properties of each graph. We then examine bisection width, path overlap, and several other properties that affect routing and resilience of peertopeer networks. Having confirmed that de Bruijn graphs offer the best diameter and highest connectivity among the existing peertopeer structures, we offer a very simple incremental building process that preserves optimal properties of de Bruijn graphs under uniform user joins/departures. We call the combined peertopeer architecture
Kronecker Graphs: An Approach to Modeling Networks
 JOURNAL OF MACHINE LEARNING RESEARCH 11 (2010) 9851042
, 2010
"... How can we generate realistic networks? In addition, how can we do so with a mathematically tractable model that allows for rigorous analysis of network properties? Real networks exhibit a long list of surprising properties: Heavy tails for the in and outdegree distribution, heavy tails for the ei ..."
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Cited by 123 (3 self)
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How can we generate realistic networks? In addition, how can we do so with a mathematically tractable model that allows for rigorous analysis of network properties? Real networks exhibit a long list of surprising properties: Heavy tails for the in and outdegree distribution, heavy tails for the eigenvalues and eigenvectors, small diameters, and densification and shrinking diameters over time. Current network models and generators either fail to match several of the above properties, are complicated to analyze mathematically, or both. Here we propose a generative model for networks that is both mathematically tractable and can generate networks that have all the above mentioned structural properties. Our main idea here is to use a nonstandard matrix operation, the Kronecker product, to generate graphs which we refer to as “Kronecker graphs”. First, we show that Kronecker graphs naturally obey common network properties. In fact, we rigorously prove that they do so. We also provide empirical evidence showing that Kronecker graphs can effectively model the structure of real networks. We then present KRONFIT, a fast and scalable algorithm for fitting the Kronecker graph generation model to large real networks. A naive approach to fitting would take superexponential
PowerLaws and the ASlevel Internet Topology
 IEEE/ACM Transactions on Networking
, 2003
"... In this paper, we study and characterize the topology of the Internet at the Autonomous System level. First, we show that the topology can be described efficiently with powerlaws. The elegance and simplicity of the powerlaws provide a novel perspective into the seemingly uncontrolled Internet struc ..."
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Cited by 109 (11 self)
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In this paper, we study and characterize the topology of the Internet at the Autonomous System level. First, we show that the topology can be described efficiently with powerlaws. The elegance and simplicity of the powerlaws provide a novel perspective into the seemingly uncontrolled Internet structure. Second, we show that powerlaws appear consistently over the last 5 years. We also observe that the powerlaws hold even in the most recent and more complete topology [10] with correlation coefficient above 99% for the degree powerlaw. In addition, we study the evolution of the powerlaw exponents over the 5 year interval and observe a variation for the degree based powerlaw of less than 10%. Third, we provide relationships between the exponents and other topological metrics.