Results 1  10
of
37
Greedy Routing with Bounded Stretch
"... Abstract—Greedy routing is a novel routing paradigm where messages are always forwarded to the neighbor that is closest to the destination. Our main result is a polynomialtime algorithm that embeds combinatorial unit disk graphs (CUDGs – a CUDG is a UDG without any geometric information) into O(log ..."
Abstract

Cited by 29 (0 self)
 Add to MetaCart
(Show Context)
Abstract—Greedy routing is a novel routing paradigm where messages are always forwarded to the neighbor that is closest to the destination. Our main result is a polynomialtime algorithm that embeds combinatorial unit disk graphs (CUDGs – a CUDG is a UDG without any geometric information) into O(log 2 n)dimensional space, permitting greedy routing with constant stretch. To the best of our knowledge, this is the first greedy embedding with stretch guarantees for this class of networks. Our main technical contribution involves extracting, in polynomial time, a constant number of isometric and balanced tree separators from a given CUDG. We do this by extending the celebrated LiptonTarjan separator theorem for planar graphs to CUDGs. Our techniques extend to other classes of graphs; for example, for general graphs, we obtain an O(log n)stretch greedy embedding into O(log 2 n)dimensional space. The greedy embeddings constructed by our algorithm can also be viewed as a constantstretch compact routing scheme in which each node is assigned an O(log 3 n)bit label. To the best of our knowledge, this result yields the best known stretchspace tradeoff for compact routing on CUDGs. Extensive simulations on random wireless networks indicate that the average routing overhead is about 10%; only few routes have a stretch above 1.5. I.
Distributed ImageBased 3D Localization of Camera Sensor Networks
"... Abstract — We consider the problem of distributed estimation of the poses of N cameras in a camera sensor network using image measurements only. The relative rotation and translation (up to a scale factor) between pairs of neighboring cameras can be estimated using standard computer vision technique ..."
Abstract

Cited by 26 (4 self)
 Add to MetaCart
(Show Context)
Abstract — We consider the problem of distributed estimation of the poses of N cameras in a camera sensor network using image measurements only. The relative rotation and translation (up to a scale factor) between pairs of neighboring cameras can be estimated using standard computer vision techniques. However, due to noise in the image measurements, these estimates may not be globally consistent. We address this problem by minimizing a cost function on SE(3) N in a distributed fashion using a generalization of the classical consensus algorithm for averaging Euclidean data. We also derive a condition for convergence, which relates the stepsize of the consensus algorithm and the degree of the camera network graph. While our methods are designed with the camera sensor network application in mind, our results are applicable to other localization problems in a more general setting. We also provide synthetic simulations to test the validity of our approach. I.
Sensor network localization by eigenvector synchronization over the Euclidean group
 In press
"... We present a new approach to localization of sensors from noisy measurements of a subset of their Euclidean distances. Our algorithm starts by finding, embedding and aligning uniquely realizable subsets of neighboring sensors called patches. In the noisefree case, each patch agrees with its global ..."
Abstract

Cited by 25 (15 self)
 Add to MetaCart
(Show Context)
We present a new approach to localization of sensors from noisy measurements of a subset of their Euclidean distances. Our algorithm starts by finding, embedding and aligning uniquely realizable subsets of neighboring sensors called patches. In the noisefree case, each patch agrees with its global positioning up to an unknown rigid motion of translation, rotation and possibly reflection. The reflections and rotations are estimated using the recently developed eigenvector synchronization algorithm, while the translations are estimated by solving an overdetermined linear system. The algorithm is scalable as the number of nodes increases, and can be implemented in a distributed fashion. Extensive numerical experiments show that it compares favorably to other existing algorithms in terms of robustness to noise, sparse connectivity and running time. While our approach is applicable to higher dimensions, in the current paper we focus on the two dimensional case.
Distributed localization using noisy distance and angle information
 PROCEEDINGS OF THE SEVENTH ACM INTERNATIONAL SYMPOSIUM ON MOBILE AD HOC NETWORKING AND COMPUTING
, 2006
"... Localization is an important and extensively studied problem in adhoc wireless sensor networks. Given the connectivity graph of the sensor nodes, along with additional local information (e.g. distances, angles, orientations etc.), the goal is to reconstruct the global geometry of the network. In th ..."
Abstract

Cited by 20 (5 self)
 Add to MetaCart
Localization is an important and extensively studied problem in adhoc wireless sensor networks. Given the connectivity graph of the sensor nodes, along with additional local information (e.g. distances, angles, orientations etc.), the goal is to reconstruct the global geometry of the network. In this paper, we study the problem of localization with noisy distance and angle information. With no noise at all, the localization problem with both angle (with orientation) and distance information is trivial. However, in the presence of even a small amount of noise, we prove that the localization problem is NPhard. Localization with accurate distance information and relative angle information is also hard. These hardness results motivate our study of approximation schemes. We relax the nonconvex constraints to approximating convex constraints and propose linear programs (LP) for two formulations of the resulting localization problem, which we call the weak deployment and strong deployment problems. These two formulations give upper and lower bounds on the location uncertainty respectively: No sensor is located outside its weak deployment region, and each sensor can be anywhere in its strong deployment region without violating the approximate distance and angle constraints. Though LPbased algorithms are usually solved by centralized methods, we propose distributed, iterative methods, which are provably convergent to the centralized algorithm solutions. We give simulation results for the distributed algorithms, evaluating the convergence rate, dependence on measurement noises, and robustness to link dynamics.
An AsRigidAsPossible Approach to Sensor Network Localization
"... We present a novel approach to localization of sensors in a network given a subset of noisy intersensor distances. The algorithm is based on “stitching” together local structures by solving an optimization problem requiring the structures to fit together in an “AsRigidAsPossible ” manner, hence ..."
Abstract

Cited by 17 (3 self)
 Add to MetaCart
We present a novel approach to localization of sensors in a network given a subset of noisy intersensor distances. The algorithm is based on “stitching” together local structures by solving an optimization problem requiring the structures to fit together in an “AsRigidAsPossible ” manner, hence the name ARAP. The local structures consist of reference “patches” and reference triangles, both obtained from intersensor distances. We elaborate on the relationship between the ARAP algorithm and other stateoftheart algorithms, and provide experimental results demonstrating that ARAP is significantly less sensitive to sparse connectivity and measurement noise. We also show how ARAP may be distributed.
Sensor networks continue to puzzle: Selected open problems
 In Proc. 9th Internat. Conf. Distributed Computing and Networking (ICDCN
, 2008
"... Abstract. While several important problems in the field of sensor networks have already been tackled, there is still a wide range of challenging, open problems that merit further attention. We present five theoretical problems that we believe to be essential to understanding sensor networks. The goa ..."
Abstract

Cited by 14 (0 self)
 Add to MetaCart
(Show Context)
Abstract. While several important problems in the field of sensor networks have already been tackled, there is still a wide range of challenging, open problems that merit further attention. We present five theoretical problems that we believe to be essential to understanding sensor networks. The goal of this work is both to summarize the current state of research and, by calling attention to these fundamental problems, to spark interest in the networking community to attend to these and related problems in sensor networks.
Eigenvector synchronization, graph rigidity and the molecule problem
, 2012
"... ..."
(Show Context)
Monotone Percolation and the Topology Control of Wireless Networks
 45TH ANNUAL IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS
, 2004
"... This paper addresses the topology control problem for large wireless networks that are modelled by an infinite point process on a twodimensional plane. Topology control is the process of determining the edges in the network by adjusting the transmission radii of the nodes. Topology control algorit ..."
Abstract

Cited by 10 (1 self)
 Add to MetaCart
This paper addresses the topology control problem for large wireless networks that are modelled by an infinite point process on a twodimensional plane. Topology control is the process of determining the edges in the network by adjusting the transmission radii of the nodes. Topology control algorithms should be based on local decisions, be adaptive to changes, guarantee full connectivity and support efficient routing. We present a family of topology control algorithms that, respectively, achieve some or all of these requirements efficiently. The key idea in our algorithms is a concept that we call monotone percolation. In classical percolation theory, we are interested in the emergence of an infinitely large connected component. In contrast, in monotone percolation we are interested in the existence of a relatively short path that makes monotonic progress between any pair of source and destination nodes. Our key contribution is that we demonstrate how local decisions on the transmission radii can lead to monotone percolation and in turn to efficient topology control algorithms.
PATCHWORK: Efficient Localization for Sensor Networks by Distributed Global Optimization
, 2005
"... We describe a new algorithm for sensor network localization based on short intersensor distances and fully decentralized computation. The algorithm computes local coordinates of small “patches ” of sensors and glues them together using a distributed global optimization process. Thanks to the global ..."
Abstract

Cited by 10 (3 self)
 Add to MetaCart
(Show Context)
We describe a new algorithm for sensor network localization based on short intersensor distances and fully decentralized computation. The algorithm computes local coordinates of small “patches ” of sensors and glues them together using a distributed global optimization process. Thanks to the global optimization, our method is more robust in the presence of noisy measurements than existing incremental methods. Most notably, and unlike some other global optimization techniques, our method cannot be fooled by local minima that might lead to foldovers in the network layout. The method is anchorfree, so advance knowledge about locations of some sensors is not required. Nonetheless, we provide a way to take advantage of known locations of any number of anchors. An experimental study shows the effectiveness of the new algorithm in noisy environments where the sensors are distributed over regions with a variety of geometric shapes. 1.