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223
Towards IP geolocation using delay and topology measurements
 In IMC
, 2006
"... We present Topologybased Geolocation (TBG), a novel approach to estimating the geographic location of arbitrary Internet hosts. We motivate our work by showing that 1) existing approaches, based on endtoend delay measurements from a set of landmarks, fail to outperform much simpler techniques, an ..."
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Cited by 67 (8 self)
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We present Topologybased Geolocation (TBG), a novel approach to estimating the geographic location of arbitrary Internet hosts. We motivate our work by showing that 1) existing approaches, based on endtoend delay measurements from a set of landmarks, fail to outperform much simpler techniques, and 2) the error of these approaches is strongly determined by the distance to the nearest landmark, even when triangulation is used to combine estimates from different landmarks. Our approach improves on these earlier techniques by leveraging network topology, along with measurements of network delay, to constrain host position. We convert topology and delay data into a set of constraints, then solve for router and host locations simultaneously. This approach improves the consistency of location estimates, reducing the error substantially for structured networks in our experiments on Abilene and Sprint. For networks with insufficient structural constraints, our techniques integrate external hints that are validated using measurements before being trusted. Together, these techniques lower the median estimation error for our universitybased dataset to 67 km vs. 228 km for the best previous approach.
Localization in sparse networks using sweeps
 in Proceedings of ACM MobiCom
, 2006
"... Determining node positions is essential for many nextgeneration network functionalities. Previous localization algorithms lack correctness guarantees or require network density higher than required for unique localizability. In this paper, we describe a class of algorithms for finegrained localiza ..."
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Cited by 60 (6 self)
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Determining node positions is essential for many nextgeneration network functionalities. Previous localization algorithms lack correctness guarantees or require network density higher than required for unique localizability. In this paper, we describe a class of algorithms for finegrained localization called Sweeps. Sweeps correctly finitely localizes all nodes in bilateration networks. Sweeps also handles angle measurements and noisy measurements. We demonstrate the practicality of our algorithm through extensive simulations on a large number of networks, upon which it consistently localizes onethousandnode networks of average degree less than five in less than two minutes on a consumer PC.
Network localization in partially localizable networks
 IN PROCEEDINGS OF IEEE INFOCOM
, 2005
"... Knowing the positions of the nodes in a network is essential to many next generation pervasive and sensor network functionalities. Although many network localization systems have recently been proposed and evaluated, there has been no systematic study of partially localizable networks, i.e., netwo ..."
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Cited by 59 (10 self)
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Knowing the positions of the nodes in a network is essential to many next generation pervasive and sensor network functionalities. Although many network localization systems have recently been proposed and evaluated, there has been no systematic study of partially localizable networks, i.e., networks in which there exist nodes whose positions cannot be uniquely determined. There is no existing study which correctly identifies precisely which nodes in a network are uniquely localizable and which are not. This absence of a sufficient uniqueness condition permits the computation of erroneous positions that may in turn lead applications to produce flawed results. In this paper, in addition to demonstrating the relevance of networks that may not be fully localizable, we design the first framework for two dimensional network localization with an efficient component to correctly determine which nodes are localizable and which are not. Implementing this system, we conduct comprehensive evaluations of network localizability, providing guidelines for both network design and deployment. Furthermore, we study an integration of traditional geographic routing with geographic routing over virtual coordinates in the partially localizable network setting. We show that this novel crosslayer integration yields good performance, and argue that such optimizations will be likely be necessary to ensure acceptable application performance in partially localizable networks.
Virtual Coordinates for Ad hoc and Sensor Networks
, 2004
"... In many applications of wireless ad hoc and sensor networks, positionawareness is of great importance. Often, as in the case of geometric routing, it is sufficient to have virtual coordinates, rather than real coordinates. In this paper, we address the problem of obtaining virtual coordinates based ..."
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Cited by 58 (9 self)
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In many applications of wireless ad hoc and sensor networks, positionawareness is of great importance. Often, as in the case of geometric routing, it is sufficient to have virtual coordinates, rather than real coordinates. In this paper, we address the problem of obtaining virtual coordinates based on connectivity information. In particular, we propose the first approximation algorithm for this problem and discuss implementational aspects.
Approximation bounds for quadratic optimization with homogeneous quadratic constraints
 SIAM J. Optim
, 2007
"... Abstract. We consider the NPhard problem of finding a minimum norm vector in ndimensional real or complex Euclidean space, subject to m concave homogeneous quadratic constraints. We show that a semidefinite programming (SDP) relaxation for this nonconvex quadratically constrained quadratic program ..."
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Cited by 49 (24 self)
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Abstract. We consider the NPhard problem of finding a minimum norm vector in ndimensional real or complex Euclidean space, subject to m concave homogeneous quadratic constraints. We show that a semidefinite programming (SDP) relaxation for this nonconvex quadratically constrained quadratic program (QP) provides an O(m 2) approximation in the real case and an O(m) approximation in the complex case. Moreover, we show that these bounds are tight up to a constant factor. When the Hessian of each constraint function is of rank 1 (namely, outer products of some given socalled steering vectors) and the phase spread of the entries of these steering vectors are bounded away from π/2, we establish a certain “constant factor ” approximation (depending on the phase spread but independent of m and n) for both the SDP relaxation and a convex QP restriction of the original NPhard problem. Finally, we consider a related problem of finding a maximum norm vector subject to m convex homogeneous quadratic constraints. We show that an SDP relaxation for this nonconvex QP provides an O(1 / ln(m)) approximation, which is analogous to a result of Nemirovski et al. [Math. Program., 86 (1999), pp. 463–473] for the real case. Key words. semidefinite programming relaxation, nonconvex quadratic optimization, approximation bound
Localization for largescale underwater sensor networks
, 2006
"... Abstract. In this paper, we study the localization problem in largescale underwater sensor networks. The adverse aqueous environments, the node mobility, and the large network scale all pose new challenges, and most current localization schemes are not applicable. We propose a hierarchical approach ..."
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Cited by 47 (6 self)
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Abstract. In this paper, we study the localization problem in largescale underwater sensor networks. The adverse aqueous environments, the node mobility, and the large network scale all pose new challenges, and most current localization schemes are not applicable. We propose a hierarchical approach which divides the whole localization process into two subprocesses: anchor node localization and ordinary node localization. Many existing techniques can be used in the former. For the ordinary node localization process, we propose a distributed localization scheme which novelly integrates a 3dimensional Euclidean distance estimation method with a recursive location estimation method. Simulation results show that our proposed solution can achieve high localization coverage with relatively small localization error and low communication overhead in largescale 3dimensional underwater sensor networks. 1
A distributed method for solving semidefinite programs arising from ad hoc wireless sensor network localization,” Multiscale optimization methods and applications,
, 2006
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Further relaxation of the semidefinite programming approach to sensor network localization
 SIAM Journal on Optimization
, 2008
"... Abstract. Recently, a semidefinite programming (SDP) relaxation approach has been proposed to solve the sensor network localization problem. Although it achieves high accuracy in estimating the sensor locations, the speed of the SDP approach is not satisfactory for practical applications. In this pa ..."
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Cited by 41 (3 self)
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Abstract. Recently, a semidefinite programming (SDP) relaxation approach has been proposed to solve the sensor network localization problem. Although it achieves high accuracy in estimating the sensor locations, the speed of the SDP approach is not satisfactory for practical applications. In this paper we propose methods to further relax the SDP relaxation, more precisely, to relax the single semidefinite matrix cone into a set of smallsize semidefinite submatrix cones, which we call a subSDP (SSDP) approach. We present two such relaxations. Although they are weaker than the original SDP relaxation, they retain the key theoretical property, and numerical experiments show that they are both efficient and accurate. The speed of the SSDP is even faster than that of other approaches based on weaker relaxations. The SSDP approach may also pave a way to efficiently solving general SDP problems without sacrificing the solution quality.
Approximation Accuracy, Gradient Methods, and Error Bound for Structured Convex Optimization
, 2009
"... Convex optimization problems arising in applications, possibly as approximations of intractable problems, are often structured and large scale. When the data are noisy, it is of interest to bound the solution error relative to the (unknown) solution of the original noiseless problem. Related to this ..."
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Cited by 38 (1 self)
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Convex optimization problems arising in applications, possibly as approximations of intractable problems, are often structured and large scale. When the data are noisy, it is of interest to bound the solution error relative to the (unknown) solution of the original noiseless problem. Related to this is an error bound for the linear convergence analysis of firstorder gradient methods for solving these problems. Example applications include compressed sensing, variable selection in regression, TVregularized image denoising, and sensor network localization.
Scalable Localization with Mobility Prediction for Underwater Sensor Networks
"... Abstract—Due to adverse aqueous environments, nonnegligible node mobility and large network scale, localization for largescale mobile underwater sensor networks is very challenging. In this paper, by utilizing the predictable mobility patterns of underwater objects, we propose a scheme, called Sca ..."
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Cited by 36 (7 self)
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Abstract—Due to adverse aqueous environments, nonnegligible node mobility and large network scale, localization for largescale mobile underwater sensor networks is very challenging. In this paper, by utilizing the predictable mobility patterns of underwater objects, we propose a scheme, called Scalable Localization scheme with Mobility Prediction (SLMP), for underwater sensor networks. In SLMP, localization is performed in a hierarchical way, and the whole localization process is divided into two parts: anchor node localization and ordinary node localization. During the localization process, every node predicts its future mobility pattern according to its past known location information, and it can estimate its future location based on its predicted mobility pattern. Anchor nodes with known locations in the network will control the whole localization process in order to balance the tradeoff between localization accuracy, localization coverage and communication cost. We conduct extensive simulations, and our results show that SLMP can greatly reduce localization communication cost while maintaining relatively high localization coverage and localization accuracy. I.