Results 1  10
of
85
Boundary Recognition in Sensor Networks by Topological Me ods
 in Proc. of MOBICOM
, 2006
"... Wireless sensor networks are tightly associated with the underlying environment in which the sensors are deployed. The global topology of the network is of great importance to both sensor network applications and the implementation of networking functionalities. In this paper we study the problem ..."
Abstract

Cited by 106 (17 self)
 Add to MetaCart
(Show Context)
Wireless sensor networks are tightly associated with the underlying environment in which the sensors are deployed. The global topology of the network is of great importance to both sensor network applications and the implementation of networking functionalities. In this paper we study the problem of topology discovery, in particular, identifying boundaries in a sensor network. Suppose a large number of sensor nodes are scattered in a geometric region, with nearby nodes communicating with each other directly. Our goal is to find the boundary nodes by using only connectivity information. We do not assume any knowledge of the node locations or interdistances, nor do we enforce that the communication graph follows the unit disk graph model. We propose a simple, distributed algorithm that correctly detects nodes on the boundaries and connects them into meaningful boundary cycles. We obtain as a byproduct the medial axis of the sensor field, which has applications in creating virtual coordinates for routing. We show by extensive simulation that the algorithm gives good results even for networks with low density. We also prove rigorously the correctness of the algorithm for continuous geometric domains.
GromovHausdorff Stable Signatures for Shapes Using Persistence
, 2009
"... We introduce a family of signatures for finite metric spaces, possibly endowed with real valued functions, based on thepersistencediagramsofsuitablefiltrationsbuilton topofthesespaces.Weprovethestabilityofoursignatures under GromovHausdorff perturbations of the spaces. We also extend these results ..."
Abstract

Cited by 32 (5 self)
 Add to MetaCart
We introduce a family of signatures for finite metric spaces, possibly endowed with real valued functions, based on thepersistencediagramsofsuitablefiltrationsbuilton topofthesespaces.Weprovethestabilityofoursignatures under GromovHausdorff perturbations of the spaces. We also extend these results to metric spaces equipped with measures. Our signatures are wellsuited for the study of unstructured point cloud data, which we illustrate through an application in shape classification.
Distributed coverage verification in sensor networks without location information
 IEEE TRANSACTIONS ON AUTOMATIC CONTROL
, 2008
"... ..."
(Show Context)
Control Using Higher Order Laplacians in Network Topologies
 Proc. of 17th International Symposium on Mathematical Theory of Networks and Systems, Kyoto
, 2006
"... This paper establishes the proper notation and precise interpretation for Laplacian flows on simplicial complexes. In particular, we have shown how to interpret these flows as timevarying discrete differential forms that converge to harmonic forms. The stability properties of the corresponding dyna ..."
Abstract

Cited by 24 (3 self)
 Add to MetaCart
(Show Context)
This paper establishes the proper notation and precise interpretation for Laplacian flows on simplicial complexes. In particular, we have shown how to interpret these flows as timevarying discrete differential forms that converge to harmonic forms. The stability properties of the corresponding dynamical system are shown to be related to the topological structure of the underlying simplicial complex. Finally, we discuss the relevance of these results in the context of networked control and sensing. I.
Lifetime and Coverage Guarantees Through Distributed CoordinateFree Sensor Activation
"... Wireless Sensor Networks are emerging as a key sensing technology, with diverse military and civilian applications. In these networks, a large number of sensors perform distributed sensing of a target field. Each sensor is a small batteryoperated device that can sense events of interest in its sens ..."
Abstract

Cited by 20 (0 self)
 Add to MetaCart
(Show Context)
Wireless Sensor Networks are emerging as a key sensing technology, with diverse military and civilian applications. In these networks, a large number of sensors perform distributed sensing of a target field. Each sensor is a small batteryoperated device that can sense events of interest in its sensing range and can communicate with neighboring sensors. A sensor cover is a subset of the set of all sensors such that every point in the target field is in the interior of the sensing ranges of at least k different sensors in the subset, where k is a given positive integer. The lifetime of the network is the time from the point the network starts operation until the set of all sensors with nonzero remaining energy does not constitute a sensor cover. An important goal in sensor networks is to design a schedule, that is, a sequence
X.: Finegrained boundary recognition in wireless ad hoc and sensor networks by topological methods
 In: MobiHoc ’09: Proceedings of the tenth ACM international
, 2009
"... Finegrained boundary recognition in wireless ad hoc and sensor networks by topological methods ..."
Abstract

Cited by 17 (3 self)
 Add to MetaCart
Finegrained boundary recognition in wireless ad hoc and sensor networks by topological methods
Lightweight Contour Tracking in Wireless Sensor Networks
"... Abstract—We study the problem of contour tracking with binary sensors, an important problem for monitoring spatial signals and tracking group targets. In particular, we track the boundaries of the blobs of interest and capture the topological changes as the blobs merge or split. Only the nodes on th ..."
Abstract

Cited by 13 (2 self)
 Add to MetaCart
(Show Context)
Abstract—We study the problem of contour tracking with binary sensors, an important problem for monitoring spatial signals and tracking group targets. In particular, we track the boundaries of the blobs of interest and capture the topological changes as the blobs merge or split. Only the nodes on the boundaries of these deformable blobs stay active and the repair cost is proportional to the size of the contour changes. Our algorithm is completely distributed, requires only local information, and yet captures the global topological properties. The algorithm performs a fundamental monitoring function and is a foundation for further information processing of spatial sensor data. I.
CASE: Connectivitybased Skeleton Extraction in Wireless Sensor Networks
, 2009
"... Many sensor network applications are tightly coupled with the geometric environment where the sensor nodes are deployed. The topological skeleton extraction has shown great impact on the performance of such services as location, routing, and path planning in sensor networks. Nonetheless, current stu ..."
Abstract

Cited by 13 (9 self)
 Add to MetaCart
Many sensor network applications are tightly coupled with the geometric environment where the sensor nodes are deployed. The topological skeleton extraction has shown great impact on the performance of such services as location, routing, and path planning in sensor networks. Nonetheless, current studies focus on using skeleton extraction for various applications in sensor networks. How to achieve a better skeleton extraction has not been thoroughly investigated. There are studies on skeleton extraction from the computer vision community; their centralized algorithms for continuous space, however, is not immediately applicable for the discrete and distributed sensor networks. In this paper we present CASE: a novel ConnectivitybAsed Skeleton Extraction algorithm to compute skeleton graph that is robust to noise, and accurate in preservation of the original topology. In addition, no centralized operation is required. The skeleton graph is extracted by partitioning the boundary of the sensor network to identify the skeleton points, then generating the skeleton arcs, connecting these arcs, and finally refining the coarse skeleton graph. Our evaluation shows that CASE is able to extract a wellconnected skeleton graph in the presence of significant noise and shape variations, and outperforms stateoftheart algorithms.
Simplicial homology of random configurations
 Advances in Applied Probability
, 2013
"... Abstract. Given a Poisson process on a ddimensional torus, its random geometric simplicial complex is the complex whose vertices are the points of the Poisson process and simplices are given by the C̆ech complex associated to the coverage of each point. By means of Malliavin calculus, we compute e ..."
Abstract

Cited by 12 (4 self)
 Add to MetaCart
(Show Context)
Abstract. Given a Poisson process on a ddimensional torus, its random geometric simplicial complex is the complex whose vertices are the points of the Poisson process and simplices are given by the C̆ech complex associated to the coverage of each point. By means of Malliavin calculus, we compute explicitly the three first order moments of the number of ksimplices, and provide a way to compute higher order moments. Then, we derive the mean and the variance of the Euler characteristic. Using the Stein method, we estimate the speed of convergence of the number of occurrences of any connected subcomplex converges towards the Gaussian law when the intensity of the Poisson point process tends to infinity. We use a concentration inequality for Poisson processes to find bounds for the tail distribution of the Betti number of first order and the Euler characteristic in such simplicial complexes. 1.
Geodesic Delaunay triangulation and witness complex in the plane
 PROC. 18TH ACMSIAM SYMPOS. ON DISCRETE ALGORITHMS
, 2008
"... ..."
(Show Context)