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17
Compressive sensing over graphs
 in Proc. IEEE INFOCOM
, 2011
"... Abstract—In this paper, motivated by network inference and tomography applications, we study the problem of compressive sensing for sparse signal vectors over graphs. In particular, we are interested in recovering sparse vectors representing the properties of the edges from a graph. Unlike existing ..."
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Cited by 32 (3 self)
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Abstract—In this paper, motivated by network inference and tomography applications, we study the problem of compressive sensing for sparse signal vectors over graphs. In particular, we are interested in recovering sparse vectors representing the properties of the edges from a graph. Unlike existing compressive sensing results, the collective additive measurements we are allowed to take must follow connected paths over the underlying graph. For a sufficiently connected graph with n nodes, it is shown that, using O(k log(n)) path measurements, we are able to recover any ksparse link vector (with no more than k nonzero elements), even though the measurements have to follow the graph path constraints. We mainly show that the computationally efficient 1 minimization can provide theoretical guarantees for inferring such ksparse vectors with O(k log(n)) path measurements from the graph. I.
Sparse Recovery with Graph Constraints: Fundamental Limits and Measurement Construction
, 2012
"... ... with graph constraints in the sense that we can take additive measurements over nodes only if they induce a connected subgraph. We provide explicit measurement constructions for several special graphs. A general measurement construction algorithm is also proposed and evaluated. For any given gra ..."
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Cited by 14 (3 self)
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... with graph constraints in the sense that we can take additive measurements over nodes only if they induce a connected subgraph. We provide explicit measurement constructions for several special graphs. A general measurement construction algorithm is also proposed and evaluated. For any given graph G with n nodes, we derive order optimal upper bounds of the minimum number of measurements needed to recoverany ksparse vector over G (M G k,n). Our study suggests that M G k,n may serve as a graph connectivity metric.
On Identifying Additive Link Metrics Using Linearly Independent Cycles and Paths
 ACCEPTED FOR PUBLICATION IN IEEE/ACM TRANSACTIONS ON NETOWRKING
, 2011
"... In this paper, we study the problem of identifying constant additive link metrics using linearly independent monitoring cycles and paths. A monitoring cycle starts and ends at the same monitoring station while a monitoring path starts and ends at distinct monitoring stations. We show that three edge ..."
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Cited by 11 (1 self)
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In this paper, we study the problem of identifying constant additive link metrics using linearly independent monitoring cycles and paths. A monitoring cycle starts and ends at the same monitoring station while a monitoring path starts and ends at distinct monitoring stations. We show that three edge connectivity is a necessary and sufficient condition to identify link metrics using one monitoring station and employing monitoring cycles. We develop a polynomial time algorithm to compute the set of linearly independent cycles. For networks that are less than threeedge connected, we show how the minimum number of monitors required and their placement may be computed. For networks with symmetric directed links, we show the relationship between the number of monitors employed, the number of directed links for which metric is known a priori, and the identifiability for the remaining links. To the best of our knowledge, this is the first work that derives the necessary and sufficient conditions on the network topology for identifying additive link metrics and develops a polynomial time algorithm to compute linearly independent cycles and paths.
A model and algorithm for selfadaptation in serviceoriented systems
 In IEEE European Conference on Web Services (ECOWS
"... Abstract—In this paper, we address the problem of selfadaptation in internetscale serviceoriented systems. Services need to adapt by select the best neighboring services solely based on local, limited information. In such complex systems, the global significance of the various selection parameters ..."
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Cited by 4 (2 self)
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Abstract—In this paper, we address the problem of selfadaptation in internetscale serviceoriented systems. Services need to adapt by select the best neighboring services solely based on local, limited information. In such complex systems, the global significance of the various selection parameters dynamically changes. We introduce a novel metric measuring the distribution and potential impact of service properties affecting such selection parameters. We further present an formalism identifying the most significant properties based on aggregated service interaction data. We ultimately provide a ranking algorithm exploiting these dynamic interaction characteristics. Experimental evaluation demonstrates scalability and adaptiveness of our approach. I.
On the Maximum Number of Linearly Independent Cycles and Paths in a Network
, 2012
"... We consider the problem of identifying additive link metrics in an arbitrary undirected network using measurement nodes and establishing paths/cycles between them. For a given placement of measurement nodes, we define and derive the “link rank” of the network—the maximum number of linearly independe ..."
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Cited by 3 (0 self)
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We consider the problem of identifying additive link metrics in an arbitrary undirected network using measurement nodes and establishing paths/cycles between them. For a given placement of measurement nodes, we define and derive the “link rank” of the network—the maximum number of linearly independent cycles/paths that may be established between the measurement nodes. We develop a polynomial time algorithm to compute a set of cycles/paths that achieves the maximum rank.
Accurate and efficient network tomography through network coding
 IEEE Trans. Vehicular Tech
, 2011
"... Abstract—Accurate and efficient measurement of networkinternal characteristics is critical for the management and maintenance of largescale networks. In this paper, we propose a linear algebraic network tomography (LANT) framework for the active inference of link loss rates on mesh topologies thr ..."
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Cited by 2 (0 self)
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Abstract—Accurate and efficient measurement of networkinternal characteristics is critical for the management and maintenance of largescale networks. In this paper, we propose a linear algebraic network tomography (LANT) framework for the active inference of link loss rates on mesh topologies through network coding. Probe packets are transmitted from the sources to the destinations along a set of paths. Intermediate nodes linearly combine the received probes and transmit the coded probes using predetermined coding coefficients. Although a smaller probe size can reduce the bandwidth usage of the network, the inference framework is not valid if the probe size falls below a certain threshold. To this end, we determine the minimum probe packet size, which is necessary and sufficient to establish the mapping between the contents of the received probes and the losses on the different sets of paths. Then, we develop algorithms to find the coding coefficients such that the minimum probe size is achieved. We propose a linear algebraic approach to develop consistent estimators of link loss rates, which converge to the actual loss rates as the number of probes increases. Simulation results show that the LANT framework achieves better estimation accuracy than the belief propagation algorithm for a large number of probe packets. Index Terms—Link loss rate estimation, network coding, network tomography. I.
Large scale probabilistic available bandwidth estimation
, 2010
"... The common utilizationbased definition of available bandwidth and many of the existing tools to estimate it suffer from several important weaknesses: i) most tools report a point estimate of average available bandwidth over a measurement interval and do not provide a confidence interval; ii) the co ..."
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Cited by 2 (0 self)
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The common utilizationbased definition of available bandwidth and many of the existing tools to estimate it suffer from several important weaknesses: i) most tools report a point estimate of average available bandwidth over a measurement interval and do not provide a confidence interval; ii) the commonly adopted models used to relate the available bandwidth metric to the measured data are invalid in almost all practical scenarios; iii) existing tools do not scale well and are not suited to the task of multipath estimation in largescale networks; iv) almost all tools use adhoc techniques to address measurement noise; and v) tools do not provide enough flexibility in terms of accuracy, overhead, latency and reliability to adapt to the requirements of various applications. In this paper we propose a new definition for available bandwidth and a novel framework that addresses these issues. We define probabilistic available bandwidth (PAB) as the largest input rate at which we can send a traffic flow along a path while achieving, with specified probability, an output rate that is almost as large as the input rate. PAB is expressed directly in terms of the measurable output rate and includes adjustable parameters that allow the user to adapt to different application requirements. Our probabilistic framework to estimate networkwide probabilistic available bandwidth is based on packet trains, Bayesian inference, factor graphs and active sampling. We deploy our tool on the PlanetLab network and our results show that we can obtain accurate estimates with a much smaller measurement overhead compared to existing approaches.
Scalable RealTime Monitoring for Distributed Applications
"... Abstract—In order to assess service quality of a networked application (such as a streaming session), distributed monitoring servers need to continuously collect applicationspecific performance metrics in real time. Much of the previous work to address this is to use distributed aggregation tree (D ..."
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Cited by 1 (0 self)
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Abstract—In order to assess service quality of a networked application (such as a streaming session), distributed monitoring servers need to continuously collect applicationspecific performance metrics in real time. Much of the previous work to address this is to use distributed aggregation tree (DAT) rooted at each monitor. However, this approach often leads to high monitoring delay and network stress. In this paper, we study a highly scalable monitoring network for distributed applications. In the network, there are distributed monitors collecting application performance in two steps: first, client applications report their performance to some proxies by means of a client overlay, and then the proxies report the performance to the distributed monitors using another proxy overlay. We first formulate the problem to construct overlays minimizing monitoring delay. The problem is shown to be NPhard. Then, we present a simple, efficient, and scalable monitoring algorithm called SMon, which continuously reduces network diameter in real time in a distributed manner. Through simulations and actual experimental measurements with implementation, we show that SMon achieves low monitoring delay, network stress, and protocol overhead for distributed applications. Index Terms—Distributed protocol, realtime network monitoring, peertopeer network, proxies Ç 1
COMPRESSED SENSING WITH CORRUPTED PARTICIPANTS
"... Compressed sensing (CS) theory promises one can recover realvalued sparse signal from a small number of linear measurements. Motivated by network monitoring with link failures, we for the first time consider the problem of recovering signals that contain both realvalued entries and corruptions, wh ..."
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Cited by 1 (1 self)
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Compressed sensing (CS) theory promises one can recover realvalued sparse signal from a small number of linear measurements. Motivated by network monitoring with link failures, we for the first time consider the problem of recovering signals that contain both realvalued entries and corruptions, where the real entries represent transmission delays on normal links and the corruptions represent failed links. Unlike conventional CS, here a measurement is realvalued only if it does not include a failed link, and it is corrupted otherwise. We prove thatO((d+1)max(d,k)logn) nonadaptive measurements are enough to recover all ndimensional signals that containk nonzero real entries anddcorruptions. We provide explicit constructions of measurements and recovery algorithms. We also analyze the performance of signal recovery when the measurements contain errors. Index Terms — compressed sensing, group testing, fundamental limits, network tomography, corruptions. We propose to locate the failed links and recover the transmission delays on normal links simultaneously from a set of nonadaptive path measurements. A path measurement is a “failure ” if it includes at least one failed link, since its packets will be lost. Otherwise, we obtain the realvalued path delay which is the sum of the link delays of links it passes through. We assume that the number of failed links and the number of nonzero link delays are both small. As far as we know, recovering sparse signals that contain failures is a new problem and has not been systematically addressed before. We for the first time consider the problem of recovering sparse signals that contain corruptions and formulate it into a combined CS and GT problem (Section 2). We provide bounds of the number of measurements needed to recover such signals (Theorem 2) and compare it with CS and GT (Table 1). We provide explicit measurement construction method as well as efficient recovery algorithms (Section 3). When the measurements are erroneous, the number of measurements needed is also characterized (Section 4). 1.
Recent results on sparse recovery over graphs.
 In Proc. Asilomar. IEEE,
, 2011
"... AbstractIn this paper, we review our recent results on sparse recovery over graphs, which was motivated by network tomography problems. Our finding has made a new connection between coding theory and graph theory. We also discuss robustness of our proposed measurement construction. I. INTRODUCTION ..."
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AbstractIn this paper, we review our recent results on sparse recovery over graphs, which was motivated by network tomography problems. Our finding has made a new connection between coding theory and graph theory. We also discuss robustness of our proposed measurement construction. I. INTRODUCTION Compressive sensing is a new paradigm in signal processing theory, which proposes to sample and recover parsimonious signals efficiently. The basic idea of compressive sensing is that if an object being measured is wellapproximated by a lower dimensional object (e.g., sparse vector, lowrank matrix, etc.) in an appropriate space, one can exploit this property to achieve perfect recovery of the object. In many of the compressive literature, there are no restrictions on how the compressive sensing matrices are constructed [3]