Topology inference in the presence of anonymous routers

Yao, B.; Viswanathan, Ramesh; Chang, Fangzhe; Waddington, Daniel

doi:10.1109/infcom.2003.1208687

Cited by 86 publications

(89 citation statements)

References 14 publications

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“…For a trace set to be generable from a network, we required that the unique identifier of every node in the network appear in at least one trace. However, on further study we learned that routers in a network appear anonymous because they are configured either to never send ICMP responses, or to use the destination addresses of the traceroute packets instead of their real addresses [10]. Thus, if a node is anonymous in a single trace, it is usually anonymous in all traces in a trace set.…”

Section: Term Definitionsmentioning

confidence: 99%

“…Hence we will adopt the same approach as Yao et al in [10] and attempt to reconstruct a topology with the smallest possible number of anonymous nodes. Accordingly, we adopt a new definition:…”

Section: Term Definitionsmentioning

confidence: 99%

“…Unfortunately, ISPs do not make maps of the true network topology publicly available. Consequently, a considerable amount of research effort has been devoted to the development of systems that reconstruct the topology of networks in the Internet from publicly available data - [10], [6], and [4].…”

Section: Introductionmentioning

confidence: 99%

“…To solve this problem, Yao et al [10] have suggested computing the minimal topology -the topology of the network with the smallest number of anonymous nodes (subject to some constraints -trace preservation and distance preservation) from which the given trace set is generable. They conclude that the problem of computing a minimal network topology from a given set of traces is NP-complete.…”

Section: Introductionmentioning

confidence: 99%

“…We now consider how our work relates to the proof of Yao [10]. The solution to our apparent conflict is that Yao et al claim NP completeness for the decision problem TOP-INF-DEC, which asks "Does there exist a network, from which trace set T is generable, and which has at most k anonymous nodes?"…”

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confidence: 99%

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On the Hardness of Topology Inference

Acharya

Gouda

2011

Distributed Computing and Networking

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Abstract. Many systems require information about the topology of networks on the Internet, for purposes like management, efficiency, testing of new protocols and so on. However, ISPs usually do not share the actual topology maps with outsiders; thus, in order to obtain the topology of a network on the Internet, a system must reconstruct it from publicly observable data. The standard method employs traceroute to obtain paths between nodes; next, a topology is generated such that the observed paths occur in the graph. However, traceroute has the problem that some routers refuse to reveal their addresses, and appear as anonymous nodes in traces. Previous research on the problem of topology inference with anonymous nodes has demonstrated that it is at best NP-complete. In this paper, we improve upon this result. In our previous research, we showed that in the special case where nodes may be anonymous in some traces but not in all traces (so all node identifiers are known), there exist trace sets that are generable from multiple topologies. This paper extends our theory of network tracing to the general case (with strictly anonymous nodes), and shows that the problem of computing the network that generated a trace set, given the trace set, has no general solution. The weak version of the problem, which allows an algorithm to output a "small" set of networks-any one of which is the correct one-is also not solvable. Any algorithm guaranteed to output the correct topology outputs at least an exponential number of networks. Our results are surprisingly robust: they hold even when the network is known to have exactly two anonymous nodes, and every node as well as every edge in the network is guaranteed to occur in some trace. On the basis of this result, we suggest that exact reconstruction of network topology requires more powerful tools than traceroute.

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Section: Term Definitionsmentioning

confidence: 99%

Section: Term Definitionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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On the Hardness of Topology Inference

Acharya

Gouda

2011

Distributed Computing and Networking

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On properties of multicast routing trees

Janic

Mieghem

2006

Int. J. Commun. Syst.

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SUMMARYIn the last several years we witnessed the proliferation of multimedia applications on the Internet. One of the unavoidable techniques to support this type of communication is multicasting. However, even a decade after its initial proposal, multicast is still not widely deployed. One of the reasons is the lack of a solid business model. If the gain and the cost of multicast could be predicted, network operators might be encouraged to deploy multicast on a larger scale. In this paper we propose analytical expressions that could be used to estimate the gain of network-layer multicast. We show that the theoretical model matches extensive simulation and Internet measurement results remarkably well.Furthermore, we examine the reliability of traceroute data and of traceroutes-based conclusions. We investigate the node degree distributions in the Internet maps obtained from CAIDA and RIPE and we show the divergency of our results with those obtained by other researchers. We further focus on the analysis of multicast trees based on traceroute data. Only few results have been available on the node degree distribution of multicast routing trees which provided contradictory conclusions. Our results seem to indicate that the node degrees follow power laws only for a large number of multicast users.

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Topology discovery of sparse random graphs with few participants

Anandkumar

Hassidim

Kelner

2012

Random Struct Algorithms

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We consider the task of topology discovery of sparse random graphs using end-to-end random measurements (e.g., delay) between a subset of nodes, referred to as the participants. The rest of the nodes are hidden, and do not provide any information for topology discovery. We consider topology discovery under two routing models: (a) the participants exchange messages along the shortest paths and obtain end-to-end measurements, and (b) additionally, the participants exchange messages along the second shortest path. For scenario (a), our proposed algorithm results in a sub-linear edit-distance guarantee using a sub-linear number of uniformly selected participants. For scenario (b), we obtain a much stronger result, and show that we can achieve consistent reconstruction when a sub-linear number of uniformly selected nodes participate. This implies that accurate discovery of sparse random graphs is tractable using an extremely small number of participants. We finally obtain a lower bound on the number of participants required by any algorithm to reconstruct the original random graph up to a given edit distance. We also demonstrate that while consistent discovery is tractable for sparse random graphs using a small number of participants, in general, there are graphs which cannot be discovered by any algorithm even with a significant number of participants, and with the availability of end-to-end information along all the paths between the participants.

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Topology inference in the presence of anonymous routers

Cited by 86 publications

References 14 publications

On the Hardness of Topology Inference

On the Hardness of Topology Inference

On properties of multicast routing trees

Topology discovery of sparse random graphs with few participants

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