## Hierarchical Inference of Unicast Network Topologies Based on End-to-End Measurements

Citations: | 2 - 0 self |

### BibTeX

@MISC{Shih_hierarchicalinference,

author = {Meng-fu Shih and Alfred O. Hero},

title = {Hierarchical Inference of Unicast Network Topologies Based on End-to-End Measurements},

year = {}

}

### OpenURL

### Abstract

Abstract—In this paper, we address the problem of topology discovery in unicast logical tree networks using end-to-end measurements. Without any cooperation from the internal routers, topology estimation can be formulated as hierarchical clustering of the leaf nodes based on pairwise correlations as similarity metrics. Unlike previous work that first assumes the network topology is a binary tree and then tries to generalize to a nonbinary tree, we provide a framework that directly deals with general logical tree topologies. A hierarchical algorithm to estimate the topology is developed in a recursive manner by finding the best partitions of the leaf nodes level by level. Our simulations show that the algorithm is more robust than binary-tree based methods. Index Terms—Graph-based clustering, mixture models, network tomography, topology estimation. I.

### Citations

1370 | Data Clustering: a Review
- Jain, Murty, et al.
- 1999
(Show Context)
Citation Context ...subgroups [6], [7]. Each leaf node itself is also considered as a cluster, called a trivial cluster. Hierarchical clustering relies on a measure of pairwise information to partition the input objects =-=[13]-=-. The objects in one (sub)cluster must be more similar to each other than to those in the remaining (sub)clusters. Suppose the similarity between a pair of leaf nodes can be expressed by some quantita... |

986 |
Finite Mixture Models
- McLachlan, Peel
- 2000
(Show Context)
Citation Context ... of internal nodes is known and the cardinality is given for each . A reasonable prior distribution of is for . Given , where denotes the Gaussian pdf, this induces a finite mixture model (see, e.g., =-=[16]-=-). A finite mixture model is generally expressed as the convex combination of probability density functions: , where Note that the model order in (1) equals the number of the internal nodes of the tre... |

324 | Simple fast algorithms for the editing distance between trees and related problems
- Zhang, Shasha
- 1989
(Show Context)
Citation Context ...n under a wide range of conditions on the magnitudes and variances of the similarity estimates. The results show that our algorithm generally achieves a lower error, as measured by tree edit distance =-=[11]-=- to the true topology, and a higher percentage of correctly estimated trees. The three candidate probing schemes are evaluated on an ns-2 1 simulated network. Monte Carlo simulations show the queueing... |

290 | Unsupervised Learning of Finite Mixture Models
- Figueiredo, Jain
- 2002
(Show Context)
Citation Context ...c value. This relaxation leaves the prior, along with other parameters in the model, to be determined, e.g., by unsupervised estimation of the mixture model. It can be achieved using the EM algorithm =-=[17]-=-, [18]. To discover the topology, the similarity sets in are determined by associating each with the component that contributes . B. MML Penalized Likelihood for the Mixture Model Likelihood-based est... |

132 |
A simple min-cut algorithm
- Stoer, Wagner
- 1997
(Show Context)
Citation Context ...he input and returns , where is a mincut of that divides into two disjoint subgraphs and . The problem of finding a mincut for a connected graph is one of the classical subjects in graph theory [22], =-=[23]-=-. The HCS algorithm recursively applies subroutine MINCUT to partition the graph until all the connected subgraphs are highly connected. The details can be found in [20]. In order to apply the HCS alg... |

107 | A clustering algorithm based on graph connectivity
- HARTUV, SHAMIR
- 2000
(Show Context)
Citation Context ...ted using graph edge weights is depicted in Fig. 4(b). Basically, any graph-based clustering algorithm for weighted graphs could work for our purpose. Here, we describe a simple algorithm proposed in =-=[20]-=-, the highly connected subgraph (HCS) algorithm. Let be a graph both undirected and weighted, where is the set of vertices and is the set of edges. Every edge in has a nonnegative real weight .Acut in... |

91 | Inference of Multicast Routing Trees and Bottleneck Bandwidths using End-to-End Measurements
- Ratnasamy, McCanne
- 1999
(Show Context)
Citation Context ... such cooperation is likely to become more difficult in the future. Due to this reason the problem of discovering the network topology based only on end-to-end measurements has been of great interest =-=[1]-=-–[8]. This type of problems belongs to the research category called network tomography. Ratnasamy et al. [1] and Duffield et al. [2] pioneered work in discovery of multicast network topologies. They s... |

77 | Maximum likelihood network topology identification from edge-based unicast measurements
- Coates, Castro, et al.
(Show Context)
Citation Context ...uristically selected threshold. The DBT algorithm has also been extended to use other metrics such as packet delays [2], [3]. Topology estimation in unicast networks was investigated by Castro et al. =-=[4]-=-–[6]. They invented a method of probing, called sandwich probes, to estimate the queueing delay on the shared path from the root to two of the leaf nodes. Castro et al. also proposed a binary tree con... |

66 | Multicast topology inference from measured end-to-end loss
- Duffield, Horowitz, et al.
(Show Context)
Citation Context ...gy based only on end-to-end measurements has been of great interest [1]–[8]. This type of problems belongs to the research category called network tomography. Ratnasamy et al. [1] and Duffield et al. =-=[2]-=- pioneered work in discovery of multicast network topologies. They specifically targeted the identification of the network’s logical tree structure. By sending multicast probes from the root node of t... |

49 |
Linear time algorithms for finding a sparse k-connected spanning subgraph of a k-connected graph”, Algorithmica 7
- Nagamochi, Ibaraki
- 1992
(Show Context)
Citation Context ...h as the input and returns , where is a mincut of that divides into two disjoint subgraphs and . The problem of finding a mincut for a connected graph is one of the classical subjects in graph theory =-=[22]-=-, [23]. The HCS algorithm recursively applies subroutine MINCUT to partition the graph until all the connected subgraphs are highly connected. The details can be found in [20]. In order to apply the H... |

43 | Inference and labeling of metric-induced network topologies
- Bestavros, Byers, et al.
- 2002
(Show Context)
Citation Context ...eaf nodes in Fig. 1 (left) and the corresponding similarity clustering tree T (C) (right). In topology estimation, the concept of metric-induced network topology (MINT) introduced by Bestavros et al. =-=[10]-=- provides a framework for defining the similarity metrics. Under the MINT framework a metric is defined which is used to capture the similarity between all measurement pairs, e.g., covariance between ... |

42 | Unsupervised Learning using MML
- Oliver
- 1996
(Show Context)
Citation Context ...e. This relaxation leaves the prior, along with other parameters in the model, to be determined, e.g., by unsupervised estimation of the mixture model. It can be achieved using the EM algorithm [17], =-=[18]-=-. To discover the topology, the similarity sets in are determined by associating each with the component that contributes . B. MML Penalized Likelihood for the Mixture Model Likelihood-based estimatio... |

41 | Multiple Source, Multiple Destination Network Tomography
- Rabbat, Nowak, et al.
- 2004
(Show Context)
Citation Context ...osed algorithm. Future work could focus on the use of hybrid probing schemes which consist of multiple types of probes. Our work could also be extended to include multiple probing sources, such as in =-=[24]-=-. Extensive real network experiments should be implemented in the future to compare to real network topologies. Fig. 7. Error tree distance versus the number of normalized similarity samples N N for t... |

29 |
and Rissanen: Intertwining themes in theories of model selection
- Lanterman
(Show Context)
Citation Context ...mber of probe trees. Hence, .Asordering of the components is irrelevant, the factorial term can be removed from the MML expression (3). We also approximate by the one-dimensional constant as in [18], =-=[19]-=-. Substituting the terms above into (3), we have where . This motivates the following hierarchical topology likelihood for a logical tree : where denotes the partition specified by the child nodes of ... |

22 | Multicast topology inference from end-to-end measurements
- eld, Horowitz, et al.
- 2000
(Show Context)
Citation Context ...nformation to identify the topology for highly congested networks. Similar comparisons showing how different types of metrics perform with different traffic load in multicast networks can be found in =-=[15]-=-. , and is an arbitrary pdf for . The ’s are called the mixing probabilities, and the ’s are the mixture components. is the number of mixture components in the model, often referred as the model order... |

14 | Likelihood based hierarchical clustering
- Castro, Coates, et al.
- 2004
(Show Context)
Citation Context ...mapping between them. In the model experiment, we tested the proposed HTE algorithm, along with the DBT and LBT. We fixed the range of the uniform distribution for each link metric to the region [2], =-=[6]-=-. The scale factor for sample standard deviation varied from 1 to 10 for link 16 and 17 and was fixed at for the others. Fig. 6. (a) Average tree edit distance and (b) percentage of correctly identifi... |

14 | Network tomography from measured end-to-end delay covariance
- Duffield, Presti
- 2004
(Show Context)
Citation Context ...ueueing delays of the packet pair are identical with probability 1 when they travel along the shared path. The first type of metric that can be retrieved from the packet pairs is delay variance [10], =-=[14]-=-. The independence assumption A1) implies the (queueing) delay over the shared path has a variance equal the end-to-end delay covariance of the two packets. For each probe tree we need end-to-end dela... |

8 | Network topology discovery using finite mixture models
- Shih, Hero
- 2004
(Show Context)
Citation Context ...he set of descendant leaf nodes of . Topology estimation can be formulated as hierarchical clustering of the leaf nodes in which each group of nodes may be recursively partitioned into subgroups [6], =-=[7]-=-. Each leaf node itself is also considered as a cluster, called a trivial cluster. Hierarchical clustering relies on a measure of pairwise information to partition the input objects [13]. The objects ... |

7 |
Internet Tomography: Recent Development
- Castro, Coates, et al.
- 2003
(Show Context)
Citation Context ...urements through the spread of its probability density function (pdf) [6]. The special case of Gaussian-distributed measurements was previously called the likelihood-based binary tree algorithm (LBT) =-=[5]-=-. To compensate for the greedy behavior of the ALT, causing it to reach a local optimum in many cases, as well as to extend the result to general trees without using a threshold, they introduced a Mon... |

6 | Communities in graphs - Brinkmeier - 2003 |

2 | Topology discovery on unicast networks: A hierarchical approach based on end-to-end measurements,” CSPL
- Shih, Hero
(Show Context)
Citation Context ...h cooperation is likely to become more difficult in the future. Due to this reason the problem of discovering the network topology based only on end-to-end measurements has been of great interest [1]–=-=[8]-=-. This type of problems belongs to the research category called network tomography. Ratnasamy et al. [1] and Duffield et al. [2] pioneered work in discovery of multicast network topologies. They speci... |

2 |
Hero Iii, Unicast-based inference of network link delay distributions with finite mixture models
- Shih, O
(Show Context)
Citation Context ...itting is to add model order penalties to the likelihood [19]. We adopt a criterion called MML [19] to derive the penalty function. MML has been widely used in unsupervised learning of mixture models =-=[9]-=-, [17], [18]. The incomplete data penalized log likelihood is expressed as [17] (2) (3) Authorized licensed use limited to: University of Michigan Library. Downloaded on May 5, 2009 at 11:02 from IEEE... |

1 |
Adaptive multicast topology inference,” presented at the
- Duffield, Horowitz, et al.
- 2001
(Show Context)
Citation Context ...ovement is made by any pairwise merge. We would like to point out that all the preclustering, progressive search and postmerge algorithms are heuristic. However, unlike the thresholds used in [2] and =-=[3]-=-, they are based on the probability model and likelihood function. Furthermore, our algorithms are all deterministic instead of Monte Carlo, so the convergence problem of simulated methods can be avoi... |

1 |
Unicast Internet tomography
- Shih
- 2005
(Show Context)
Citation Context ...ironments. Section VI provides the conclusion and discusses future work. For more detailed derivations and more simulation studies than what could be presented in this paper the reader is referred to =-=[12]-=-. II. BACKGROUND A. Problem Formulation Our work focuses on the problem of estimating logical tree network structures given end-to-end statistics measured by probes sent from the root to the leaf node... |