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42
On the bias of traceroute sampling: or, powerlaw degree distributions in regular graphs
 In ACM STOC
, 2005
"... Understanding the graph structure of the Internet is a crucial step for building accurate network models and designing efficient algorithms for Internet applications. Yet, obtaining this graph structure can be a surprisingly difficult task, as edges cannot be explicitly queried. For instance, empiri ..."
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Understanding the graph structure of the Internet is a crucial step for building accurate network models and designing efficient algorithms for Internet applications. Yet, obtaining this graph structure can be a surprisingly difficult task, as edges cannot be explicitly queried. For instance, empirical studies of the network of Internet Protocol (IP) addresses typically rely on indirect methods like traceroute to build what are approximately singlesource, alldestinations, shortestpath trees. These trees only sample a fraction of the network’s edges, and a recent paper by Lakhina et al. found empirically that the resulting sample is intrinsically biased. Further, in simulations, they observed that the degree distribution under traceroute sampling exhibits a power law even when the underlying degree distribution is Poisson. In this paper, we study the bias of traceroute sampling mathematically and, for a very general class of underlying degree distributions, explicitly calculate the distribution that will be observed. As example applications of our machinery, we prove that traceroute sampling finds powerlaw degree distributions in both δregular and Poissondistributed random graphs. Thus, our work puts the observations of Lakhina et al. on a rigorous footing, and extends them to nearly arbitrary degree distributions.
Internet Topology Discovery: a Survey
 IN IEEE COMMUNICATIONS SURVEY AND TUTORIALS
, 2007
"... ..."
kcore decomposition of Internet graphs: hierarchies, selfsimilarity and measurement biases
 NETWORKS AND HETEROGENEOUS MEDIA
, 2008
"... We consider the kcore decomposition of network models and Internet graphs at the autonomous system (AS) level. The kcore analysis allows to characterize networks beyond the degree distribution and uncover structural properties and hierarchies due to the specific architecture of the system. We com ..."
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We consider the kcore decomposition of network models and Internet graphs at the autonomous system (AS) level. The kcore 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 kcore 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 kcore analysis is assessed with numerical experiments simulating biased exploration on a wide range of network models. We find that the kcore analysis provides an interesting characterization of the fluctuations and incompleteness of maps as well as information helping to discriminate the original underlying structure.
Deployment of an algorithm for largescale topology discovery
 IN COMMUNICATIONS, SAMPLING THE INTERNET: TECHNIQUES AND APPLICATIONS 24(12
, 2006
"... Topology discovery systems are starting to be introduced in the form of easily and widely deployed software. Unfortunately, the research community has not examined the problem of how to perform such measurements efficiently and in a networkfriendly manner. This paper describes several contribution ..."
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Cited by 27 (7 self)
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Topology discovery systems are starting to be introduced in the form of easily and widely deployed software. Unfortunately, the research community has not examined the problem of how to perform such measurements efficiently and in a networkfriendly manner. This paper describes several contributions towards that end. These were first presented in the proceedings of ACM SIGMETRICS 2005. We show that standard topology discovery methods (e.g., skitter) are quite inefficient, repeatedly probing the same interfaces. This is a concern, because when scaled up, such methods will generate so much traffic that they will begin to resemble DDoS attacks. We propose two metrics focusing on redundancy in probing and show that both are important. We also propose and evaluate Doubletree, an algorithm that strongly reduces redundancy while maintaining nearly the same level of node and link coverage. The key ideas are to exploit the treelike structure of routes to and from a single point in order to guide when to stop probing, and to probe each path by starting near its midpoint. Following the SIGMETRICS work, we implemented Doubletree, and deployed it in a real network environment. This paper describes that implementation, as well as preliminary favorable results.
Complex network measurements: Estimating the relevance of observed properties
 In INFOCOM 2008. 27th IEEE International Conference on Computer Communications, Joint Conference of the IEEE Computer and Communications Societies
, 2008
"... Abstract—Complex networks, modeled as large graphs, received much attention during these last years. However, data on such networks is only available through intricate measurement procedures. Until recently, most studies assumed that these procedures eventually lead to samples large enough to be r ..."
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Cited by 25 (3 self)
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Abstract—Complex networks, modeled as large graphs, received much attention during these last years. However, data on such networks is only available through intricate measurement procedures. Until recently, most studies assumed that these procedures eventually lead to samples large enough to be representative of the whole, at least concerning some key properties. This has crucial impact on network modeling and simulation, which rely on these properties. Recent contributions proved that this approach may be misleading, but no solution has been proposed. We provide here the first practical way to distinguish between cases where it is indeed misleading, and cases where the observed properties may be trusted. It consists in studying how the properties of interest evolve when the sample grows, and in particular whether they reach a steady state or not.
A Radar for the Internet
 in Proc. of ADN 2008
"... Abstract. Mapping the internet’s topology is a challenge in itself, and studying its dynamics is even more difficult. Achieving this would however provide key information on the nature of the internet, crucial for modeling and simulation. Moreover, detecting anomalies in this dynamics is a key issue ..."
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Abstract. Mapping the internet’s topology is a challenge in itself, and studying its dynamics is even more difficult. Achieving this would however provide key information on the nature of the internet, crucial for modeling and simulation. Moreover, detecting anomalies in this dynamics is a key issue for security. We introduce here a new measurement approach which makes it possible to capture internet dynamics at a scale of a few minutes in a radarlike manner. By conducting and analyzing largescale measurements of this kind, we rigorously and automatically detect events in the observed dynamics, which is totally out of reach of previous approaches. Since the end of the 90s, mapping the internet as a large set of nodes and links received much attention. However, due to its distributed nature and its sheer size, accurately measuring this topology is extremely difficult. The main method to do so relies on the classical traceroute tool [8], which gives a path from a machine connected to the internet (called monitor) to any other (called destination). Such paths are composed of ip addresses of internet routers and links between them. One may then obtain a (partial) map of the internet by running traceroute from many monitors to many destinations, and merging the obtained paths, see Figure 1. For various reasons, however, this is far from trivial and the obtained maps are not satisfactory [6, 3, 4]. Therefore, much effort
On the Impact of Layer2 on Node Degree Distribution
"... The Internet topology data collected through traceroute exploration has been extensively studied in the past. In particular, a remarkable property of the Internet, the powerlaw shape of node degree distribution, drew the attention of the research community. Several studies have since questioned thi ..."
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Cited by 11 (4 self)
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The Internet topology data collected through traceroute exploration has been extensively studied in the past. In particular, a remarkable property of the Internet, the powerlaw shape of node degree distribution, drew the attention of the research community. Several studies have since questioned this property. In this paper, based on a large dataset collected using mrinfo, we show that the node degree distribution is strongly impacted by the presence of layer2 (L2) networks, such as switches. L2 devices interconnect a large number of routers, themselves being also involved in multiple L2 interconnections. Such a situation induces nodes with very high degree when analyzing the layer3 (L3) graph with traceroute probing. Considering the physical design of a network, our analysis provides a lower bound on the bias generated by using only an L3 view. We also provide a model that can be a first step towards L2 aware topology generation.
Describing and simulating internet routes
 In 4th International IFIPTC6 Networking Conference
, 2004
"... Abstract. This paper introduces relevant statistics for the description of routes in the internet, seen as a graph at the interface level. Based on the observed properties, we propose and evaluate methods for generating artificial routes suitable for simulation purposes. The work in this paper is ba ..."
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Abstract. This paper introduces relevant statistics for the description of routes in the internet, seen as a graph at the interface level. Based on the observed properties, we propose and evaluate methods for generating artificial routes suitable for simulation purposes. The work in this paper is based upon a study of over seven million route traces produced by CAIDA’s skitter infrastructure.
Network Inference from Traceroute Measurements: Internet Topology ‘Species’,’ preprint arxiv:cs/0510007
, 2005
"... Internet mapping projects generally consist in sampling the network from a limited set of sources by using traceroute probes. This methodology, akin to the merging of spanning trees from the different sources to a set of destinations, leads necessarily to a partial, incomplete map of the Internet. A ..."
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Cited by 9 (0 self)
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Internet mapping projects generally consist in sampling the network from a limited set of sources by using traceroute probes. This methodology, akin to the merging of spanning trees from the different sources to a set of destinations, leads necessarily to a partial, incomplete map of the Internet. Accordingly, determination of Internet topology characteristics from such sampled maps is in part a problem of statistical inference. Our contribution begins with the observation that the inference of many of the most basic topological quantities – including network size and degree characteristics – from traceroute measurements is in fact a version of the socalled ‘species problem ’ in statistics. This observation has important implications, since species problems are often quite challenging. We focus here on the most fundamental example of a traceroute internet species: the number of nodes in a network. Specifically,
Local and dynamic analysis of Internet multicast router topology Analyse locale et dynamique de la topologie des routeurs multicast d’Internet
"... Résumé. Nous étudions les informations qui peuvent être obtenues sur la topologie des routeurs d’Internet via des requêtes IGMP. Bien que ce mécanisme soit limité aux routeurs multicast nous montrons qu’il permet d’obtenir des informations précises sur la topologie locale des routeurs. Ces informati ..."
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Cited by 7 (1 self)
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Résumé. Nous étudions les informations qui peuvent être obtenues sur la topologie des routeurs d’Internet via des requêtes IGMP. Bien que ce mécanisme soit limité aux routeurs multicast nous montrons qu’il permet d’obtenir des informations précises sur la topologie locale des routeurs. Ces informations sont difficiles à obtenir avec les techniques classiques basées sur traceroute. De plus son faible coût permet de collecter fréquemment des informations et ainsi d’en évaluer la dynamique. Abstract. We study data on routers topology gathered using IGMP messages. Although this mechanism is limited to multicast routers we show that it allows getting precise information on the local topology of routers. This information is difficult to obtain with classical tools based on traceroute. Moreover its low cost allows to frequently collect data and to study the dynamics of this topology. I.