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Active Clustering: Robust and Efficient Hierarchical Clustering using Adaptively Selected Similarities
"... Hierarchical clustering based on pairwise similarities is a common tool used in a broad range of scientific applications. However, in many problems it may be expensive to obtain or compute similarities between the items to be clustered. This paper investigates the hierarchical clustering of N items ..."
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Hierarchical clustering based on pairwise similarities is a common tool used in a broad range of scientific applications. However, in many problems it may be expensive to obtain or compute similarities between the items to be clustered. This paper investigates the hierarchical clustering of N items based on a small subset of pairwise similarities, significantly less than the complete set of N(N − 1)/2 similarities. First, we show that if the intracluster similarities exceed intercluster similarities, then it is possible to correctly determine the hierarchical clustering from as few as 3N log N similarities. We demonstrate this order of magnitude savings in the number of pairwise similarities necessitates sequentially selecting which similarities to obtain in an adaptive fashion, rather than picking them at random. We then propose an active clustering method that is robust to a limited fraction of anomalous similarities, and show how even in the presence of these noisy similarity values we can resolve the hierarchical clustering using only O ( N log 2 N) pairwise similarities. 1
Toward the Practical Use of Network Tomography for Internet Topology Discovery
"... Abstract—Accurate and timely identification of the routerlevel topology of the Internet is one of the major unresolved problems in Internet research. Topology recovery via tomographic inference is potentially an attractive complement to standard methods that use TTLlimited probes. In this paper, we ..."
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Abstract—Accurate and timely identification of the routerlevel topology of the Internet is one of the major unresolved problems in Internet research. Topology recovery via tomographic inference is potentially an attractive complement to standard methods that use TTLlimited probes. In this paper, we describe new techniques that aim toward the practical use of tomographic inference for accurate routerlevel topology measurement. Specifically, prior tomographic techniques have required an infeasible number of probes for accurate, large scale topology recovery. We introduce a DepthFirst Search (DFS) Ordering algorithm that clusters end host probe targets based on shared infrastructure, and enables the logical tree topology of the network to be recovered accurately and efficiently. We evaluate the capabilities of our DFS Ordering topology recovery algorithm in simulation and find that our method uses 94 % fewer probes than exhaustive methods and 50 % fewer than the current stateoftheart. We also present results from a case study in the live Internet where we show that DFS Ordering can recover the logical routerlevel topology more accurately and with fewer probes than prior techniques. I.
Topology Discovery of Sparse Random Graphs With Few Participants
"... We consider the task of topology discovery of sparse random graphs using endtoend 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 discover ..."
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We consider the task of topology discovery of sparse random graphs using endtoend 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 endtoend measurements, and (b) additionally, the participants exchange messages along the second shortest path. For scenario(a), ourproposedalgorithm resultsinasublineareditdistance guarantee using a sublinear number of uniformly selected participants. For scenario (b), we obtain a much stronger result, and show that we can achieve consistent reconstruction when a sublinear numberof 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 endtoend information along all the paths between the participants.
Topology Discovery of Sparse Random Graphs With Few Participants ∗
, 2011
"... We considerthe taskoftopologydiscoveryofsparserandomgraphsusing endtoendrandom measurements(e.g., delay)between a subset ofnodes, referredto 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 ro ..."
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Cited by 3 (0 self)
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We considerthe taskoftopologydiscoveryofsparserandomgraphsusing endtoendrandom measurements(e.g., delay)between a subset ofnodes, referredto 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 endtoend measurements, and (b) additionally, the participants exchange messages along the second shortest path. For scenario (a), our proposed algorithm results in a sublinear editdistance guarantee using a sublinear number of uniformly selected participants. For scenario (b), we obtain a much stronger result, and show that we can achieve consistent reconstruction when a sublinear 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 endtoend information along all the paths between the participants.
Hierarchical clustering using randomly selected measurements
 In Proceedings of the IEEE Statistical Signal Processing Workshop
, 2012
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1 Active Clustering: Robust and Efficient Hierarchical Clustering using Adaptively Selected Similarities
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Network Topology Inference with Partial Information
"... Abstract—Full knowledge of the routing topology of the Internet is useful for a multitude of network management tasks. However, the full topology is often not known and is instead estimated using topology inference algorithms. Many of these algorithms use Traceroute to probe paths and then use the ..."
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Abstract—Full knowledge of the routing topology of the Internet is useful for a multitude of network management tasks. However, the full topology is often not known and is instead estimated using topology inference algorithms. Many of these algorithms use Traceroute to probe paths and then use the collected information to infer the topology. We perform real experiments and show that in practice routers may severely disrupt the operation of Traceroute and cause it to only provide partial information. We propose iTop, an algorithm for inferring the network topology when only partial information is available. iTop constructs a virtual topology, which overestimates the number of network components, and then repeatedly merges links in this topology to resolve it towards the structure of the true network. We perform extensive simulations to compare iTop to state of the art inference algorithms. Results show that iTop significantly outperforms previous approaches and its inferred topologies are within 5 % of the original networks for all considered metrics. Additionally, we show that the topologies inferred by iTop significantly improve the performance of fault localization algorithms when compared to other approaches. Index Terms—Topology inference, Partial information, Fault localization. I.
Networkproviderindependent Overlays for Resilience and Quality of Service
"... Overlay networks are viewed as one of the solutions addressing the inefficiency and slow evolution of the Internet and have been the subject of significant research. Most existing overlays providing resilience and/or Quality of Service (QoS) need cooperation among different network providers, but an ..."
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Overlay networks are viewed as one of the solutions addressing the inefficiency and slow evolution of the Internet and have been the subject of significant research. Most existing overlays providing resilience and/or Quality of Service (QoS) need cooperation among different network providers, but an intertrust issue arises and cannot be easily solved. In this thesis, we mainly focus on networkproviderindependent overlays and investigate their performance in providing two different types of service. Specifically, this thesis addresses the following problems: • Providerindependent overlay architecture: A providerindependent overlay framework named Resilient Overlay for MissionCritical Applications (ROMCA) is proposed. We elaborate its structure including component composition and functions and also provide several operational examples. • Overlay topology construction for providing resilience service: We investigate