Network Tomography via Compressed Sensing

Firooz, Mohammad Hamed; Roy, Sumit

doi:10.1109/glocom.2010.5684036

Cited by 50 publications

(49 citation statements)

References 23 publications

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“…When all but k link metrics are zero, compressive sensing techniques are used to identify the k non-zero link metrics [16,17]. If all link metrics are binary (normal/failed), [18] proves that the network must be (k + 2)-edge-connected to identify up to k failed links by using one monitor measuring cycles.…”

Section: Further Discussion On Related Workmentioning

confidence: 99%

Identifiability of link metrics based on end-to-end path measurements

He²,

Leung

et al. 2013

Proceedings of the 2013 Conference on Internet Measurement Conference

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We investigate the problem of identifying individual link metrics in a communication network from end-to-end path measurements, under the assumption that link metrics are additive and constant. To uniquely identify the link metrics, the number of linearly independent measurement paths must equal the number of links. Our contribution is to characterize this condition in terms of the network topology and the number/placement of monitors, under the constraint that measurement paths must be cycle-free. Our main results are: (i) it is generally impossible to identify all the link metrics by using two monitors; (ii) nevertheless, metrics of all the interior links not incident to any monitor are identifiable by two monitors if the topology satisfies a set of necessary and sufficient connectivity conditions; (iii) these conditions naturally extend to a necessary and sufficient condition for identifying all the link metrics using three or more monitors. We show that these conditions not only allow efficient identifiability tests, but also enable an efficient algorithm to place the minimum number of monitors in order to identify all link metrics. Our evaluations on both random and real topologies show that the proposed algorithm achieves identifiability using a much smaller number of monitors than a baseline solution.

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Section: Further Discussion On Related Workmentioning

confidence: 99%

Identifiability of link metrics based on end-to-end path measurements

He²,

Leung

et al. 2013

Proceedings of the 2013 Conference on Internet Measurement Conference

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show abstract

“…As for the number of required measurements for the reconstruction of k-sparse vectors with random binary measurements matrices, it has been known that O(k log n k ) measurements are required [153], [154], while it has been shown that O(k log n) measurements are needed if the binary matrix is accompanied by a graph constraint [151], [155]. Moreover, a deterministic guarantee and a designed method of the routing matrix for the reconstruction of any 1-sparse signal are provided in [149], [150], taking advantage of the knowledge on compressed sensing using expander graphs [154], [156].…”

Section: Network Tomographymentioning

confidence: 99%

“…Two major forms of network tomography are link-level parameter estimation from end-to-end measurements and end-to-end traffic intensity estimation based on link-level measurements [147]. Since the original paper of compressed sensing [3] was largely motivated by the reconstruction problem of magnetic resonance imaging (MRI), which is one of the medical tomographies [148], it is quite natural to consider application of compressed sensing to network tomography [149]- [152].…”

Section: Network Tomographymentioning

confidence: 99%

A User's Guide to Compressed Sensing for Communications Systems

Hayashi

Nagahara

Tanaka

2013

IEICE Trans. Commun.

203

110

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SUMMARYThis survey provides a brief introduction to compressed sensing as well as several major algorithms to solve it and its various applications to communications systems. We firstly review linear simultaneous equations as ill-posed inverse problems, since the idea of compressed sensing could be best understood in the context of the linear equations. Then, we consider the problem of compressed sensing as an underdetermined linear system with a prior information that the true solution is sparse, and explain the sparse signal recovery based on 1 optimization, which plays the central role in compressed sensing, with some intuitive explanations on the optimization problem. Moreover, we introduce some important properties of the sensing matrix in order to establish the guarantee of the exact recovery of sparse signals from the underdetermined system. After summarizing several major algorithms to obtain a sparse solution focusing on the 1 optimization and the greedy approaches, we introduce applications of compressed sensing to communications systems, such as wireless channel estimation, wireless sensor network, network tomography, cognitive radio, array signal processing, multiple access scheme, and networked control.

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“…In contrast, we examine online learning and we provide a detailed analysis to assess the performance of sparse approximation applied to Markov models of wireless networks. Compressed sensing-based techniques have been previously applied to estimation problems in networks [19][20][21][22][23][24]. These works address graphs related to the physical connectivity of the network, where nodes are terminals and links are specific wired or wireless links or modeled by undirected graphs.…”

Section: Introductionmentioning

confidence: 99%

Structure-based learning in wireless networks via sparse approximation

Levorato

Mitra

Goldsmith

2012

J Wireless Com Network

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A novel framework for the online learning of expected cost-to-go functions characterizing wireless networks performance is proposed. The framework is based on the observation that wireless protocols induce structured and correlated behavior of the finite state machine (FSM) modeling the operations of the network. As a result, a significant dimension reduction can be achieved by projecting the cost-to-go function on a graph wavelet basis set capturing typical sub-structures in the graph associated with the FSM. Sparse approximation with random projection is then used to identify a concise set of coefficients representing the cost-to-go function in the wavelet domain. This Compressed Sensing (CS) approach enables a considerable reduction in the number of observations needed to achieve an accurate estimate of the cost-to-go function. The proposed method is characterized via stability analysis. In particular, we prove that the standard CS approach of the Least Angle Selection and Shrinkage Operator (LASSO) will not provide stability. We also determine a connection between the structure of the FSM induced by the wireless protocols and the restricted isometry property of the effective projection matrix. Simulation results of our approximation method show that 15 wavelet functions can accurately represent a cost-to-go function defined on a state space of 2000 states. Moreover, the number of state-cost observations needed to estimate the cost-to-go function is orders of magnitude smaller than that required by traditional online learning techniques.

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Network Tomography via Compressed Sensing

Cited by 50 publications

References 23 publications

Identifiability of link metrics based on end-to-end path measurements

Identifiability of link metrics based on end-to-end path measurements

A User's Guide to Compressed Sensing for Communications Systems

Structure-based learning in wireless networks via sparse approximation

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