Results 1  10
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142
Solving the multipleinstance problem with axisparallel rectangles
 Artificial Intelligence
, 1997
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AnchorFree Distributed Localization in Sensor Networks
, 2003
"... Many sensor network applications require that each node's sensor stream be annotated with its physical location in some common coordinate system. Manual measurement and configuration methods for obtaining location don't scale and are errorprone, and equipping sensors with GPS is often expensive and ..."
Abstract

Cited by 94 (8 self)
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Many sensor network applications require that each node's sensor stream be annotated with its physical location in some common coordinate system. Manual measurement and configuration methods for obtaining location don't scale and are errorprone, and equipping sensors with GPS is often expensive and does not work in indoor and urban deployments. Sensor networks can therefore benefit from a selfconfiguring method where nodes cooperate with each other, estimate local distances to their neighbors, and converge to a consistent coordinate assignment. This paper describes a fully decentralized algorithm called AFL (AnchorFree Localization) where nodes start from a random initial coordinate assignment and converge to a consistent solution using only local node interactions. The key idea in AFL is foldfreedom, where nodes first configure into a topology that resembles a scaled and unfolded version of the true configuration, and then run a forcebased relaxation procedure.We show using extensive simulations under a variety of network sizes, node densities, and distance estimation errors that our algorithm is superior to previously proposed methods that incrementally compute the coordinates of nodes in the network, in terms of its ability to compute correct coordinates under a wider variety of conditions and its robustness to measurement errors.
Rigidity, Computation, and Randomization in Network Localization
 In Proceedings of IEEE INFOCOM ’04, Hong Kong
, 2004
"... In this paper we provide a theoretical foundation for the problem of network localization in which some nodes know their locations and other nodes determine their locations by measuring the distances to their neighbors. We construct grounded graphs to model network localization and apply graph rigid ..."
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Cited by 82 (14 self)
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In this paper we provide a theoretical foundation for the problem of network localization in which some nodes know their locations and other nodes determine their locations by measuring the distances to their neighbors. We construct grounded graphs to model network localization and apply graph rigidity theory to test the conditions for unique localizability and to construct uniquely localizable networks. We further study the computational complexity of network localization and investigate a subclass of grounded graphs where localization can be computed efficiently. We conclude with a discussion of localization in sensor networks where the sensors are placed randomly.
Global Continuation For Distance Geometry Problems
 SIAM J. OPTIMIZATION
, 1995
"... Distance geometry problems arise in the interpretation of NMR data and in the determination of protein structure. We formulate the distance geometry problem as a global minimization problem with special structure, and show that global smoothing techniques and a continuation approach for global optim ..."
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Cited by 70 (7 self)
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Distance geometry problems arise in the interpretation of NMR data and in the determination of protein structure. We formulate the distance geometry problem as a global minimization problem with special structure, and show that global smoothing techniques and a continuation approach for global optimization can be used to determine solutions of distance geometry problems with a nearly 100% probability of success.
Solving Euclidean Distance Matrix Completion Problems Via Semidefinite Programming
, 1997
"... Given a partial symmetric matrix A with only certain elements specified, the Euclidean distance matrix completion problem (IgDMCP) is to find the unspecified elements of A that make A a Euclidean distance matrix (IgDM). In this paper, we follow the successful approach in [20] and solve the IgDMCP by ..."
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Cited by 69 (14 self)
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Given a partial symmetric matrix A with only certain elements specified, the Euclidean distance matrix completion problem (IgDMCP) is to find the unspecified elements of A that make A a Euclidean distance matrix (IgDM). In this paper, we follow the successful approach in [20] and solve the IgDMCP by generalizing the completion problem to allow for approximate completions. In particular, we introduce a primaldual interiorpoint algorithm that solves an equivalent (quadratic objective function) semidefinite programming problem (SDP). Numerical results are included which illustrate the efficiency and robustness of our approach. Our randomly generated problems consistently resulted in low dimensional solutions when no completion existed.
A Theory of Network Localization
, 2004
"... In this paper we provide a theoretical foundation for the problem of network localization in which some nodes know their locations and other nodes determine their locations by measuring the distances to their neighbors. We construct grounded graphs to model network localization and apply graph rigid ..."
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Cited by 62 (6 self)
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In this paper we provide a theoretical foundation for the problem of network localization in which some nodes know their locations and other nodes determine their locations by measuring the distances to their neighbors. We construct grounded graphs to model network localization and apply graph rigidity theory to test the conditions for unique localizability and to construct uniquely localizable networks. We further study the computational complexity of network localization and investigate a subclass of grounded graphs where localization can be computed efficiently. We conclude with a discussion of localization in sensor networks where the sensors are placed randomly.
Connected Rigidity Matroids and Unique Realizations of Graphs
, 2004
"... A ddimensional framework is a straight line realization of a graph G in R d. We shall only consider generic frameworks, in which the coordinates of all the vertices of G are algebraically independent. Two frameworks for G are equivalent if corresponding edges in the two frameworks have the same le ..."
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Cited by 61 (9 self)
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A ddimensional framework is a straight line realization of a graph G in R d. We shall only consider generic frameworks, in which the coordinates of all the vertices of G are algebraically independent. Two frameworks for G are equivalent if corresponding edges in the two frameworks have the same length. A framework is a unique realization of G in R d if every equivalent framework can be obtained from it by an isometry of R d. Bruce Hendrickson proved that if G has a unique realization in R d then G is (d + 1)connected and redundantly rigid. He conjectured that every realization of a (d + 1)connected and redundantly rigid graph in R d is unique. This conjecture is true for d = 1 but was disproved by Robert Connelly for d ≥ 3. We resolve the remaining open case by showing that Hendrickson’s conjecture is true for d = 2. As a corollary we deduce that every realization of a 6connected graph as a 2dimensional generic framework is a unique realization. Our proof is based on a new inductive characterization of 3connected graphs whose rigidity matroid is connected.
A GraphConstructive Approach to Solving Systems of Geometric Constraints
 ACM TRANSACTIONS ON GRAPHICS
, 1997
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Semidefinite Programming and Integer Programming
"... We survey how semidefinite programming can be used for finding good approximative solutions to hard combinatorial optimization problems. ..."
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Cited by 48 (7 self)
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We survey how semidefinite programming can be used for finding good approximative solutions to hard combinatorial optimization problems.
Molecular Modeling Of Proteins And Mathematical Prediction Of Protein Structure
 SIAM Review
, 1997
"... . This paper discusses the mathematical formulation of and solution attempts for the socalled protein folding problem. The static aspect is concerned with how to predict the folded (native, tertiary) structure of a protein, given its sequence of amino acids. The dynamic aspect asks about the possib ..."
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Cited by 47 (4 self)
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. This paper discusses the mathematical formulation of and solution attempts for the socalled protein folding problem. The static aspect is concerned with how to predict the folded (native, tertiary) structure of a protein, given its sequence of amino acids. The dynamic aspect asks about the possible pathways to folding and unfolding, including the stability of the folded protein. From a mathematical point of view, there are several main sides to the static problem:  the selection of an appropriate potential energy function;  the parameter identification by fitting to experimental data; and  the global optimization of the potential. The dynamic problem entails, in addition, the solution of (because of multiple time scales very stiff) ordinary or stochastic differential equations (molecular dynamics simulation), or (in case of constrained molecular dynamics) of differentialalgebraic equations. A theme connecting the static and dynamic aspect is the determination and formation of...