Results 1  10
of
41
Boundary recognition in sensor networks by topological methods
 In Proc. of the ACM/IEEE International Conference on Mobile Computing and Networking (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 of ..."
Abstract

Cited by 65 (16 self)
 Add to MetaCart
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.
Distributed coverage verification in sensor networks without location information
 IEEE Transactions on Automatic Control
"... Distributed coverage verification in sensor networks without location information ..."
Abstract

Cited by 16 (0 self)
 Add to MetaCart
Distributed coverage verification in sensor networks without location information
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 12 (2 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.
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 11 (0 self)
 Add to MetaCart
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
Geodesic Delaunay triangulation and witness complex in the plane
 PROC. 18TH ACMSIAM SYMPOS. ON DISCRETE ALGORITHMS
, 2008
"... ..."
Dynamic coverage verification in mobile sensor networks via switched higher order Laplacians
 in Robotics: Science & Systems
, 2007
"... Abstract — In this paper, we study the problem of verifying dynamic coverage in mobile sensor networks using certain switched linear systems. These switched systems describe the flow of discrete differential forms on timeevolving simplicial complexes. The simplicial complexes model the connectivity ..."
Abstract

Cited by 7 (1 self)
 Add to MetaCart
Abstract — In this paper, we study the problem of verifying dynamic coverage in mobile sensor networks using certain switched linear systems. These switched systems describe the flow of discrete differential forms on timeevolving simplicial complexes. The simplicial complexes model the connectivity of agents in the network, and the homology groups of the simplicial complexes provides information about the coverage properties of the network. Our main result states that the asymptotic stability the switched linear system implies that every point of the domain covered by the mobile sensor nodes is visited infinitely often, hence verifying dynamic coverage. The enabling mathematical technique for this result is the theory of higher order Laplacian operators, which is a generalization of the graph Laplacian used in spectral graph theory and continuoustime consensus problems.
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 7 (2 self)
 Add to MetaCart
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.
Distributed Coordinatefree Algorithm for Full Sensing Coverage
 International Journal of Sensor Networks
, 2008
"... coverage ..."
Beyond Graphs: Capturing Groups in Networks
"... Abstract—Currently, the de facto representational choice for networks is graphs. A graph captures pairwise relationships (edges) between entities (vertices) in a network. Network science, however, is replete with group relationships that are more than the sum of the pairwise relationships. For examp ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
Abstract—Currently, the de facto representational choice for networks is graphs. A graph captures pairwise relationships (edges) between entities (vertices) in a network. Network science, however, is replete with group relationships that are more than the sum of the pairwise relationships. For example, collaborative teams, wireless broadcast, insurgent cells, coalitions all contain unique group dynamics that need to be captured in their respective networks. We propose the use of the (abstract) simplicial complex to model groups in networks. We show that a number of problems within social and communications networks such as networkwide broadcast and collaborative teams can be elegantly captured using simplicial complexes in a way that is not possible with graphs. We formulate combinatorial optimization problems in these areas in a simplicial setting and illustrate the applicability of topological concepts such as “Betti numbers ” in structural analysis. As an illustrative case study, we present an analysis of a realworld collaboration network, namely the ARL NSCTA network of researchers and tasks. I.
Testing contractibility in planar Rips complexes
 In Proc. Symp. on Comp. Geom. (SoCG) 2008
"... The (Vietoris)Rips complex of a discrete pointset P is an abstract simplicial complex in which a subset of P defines a simplex if and only if the diameter of that subset is at most 1. We describe an efficient algorithm to determine whether a given cycle in a planar Rips complex is contractible. Ou ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
The (Vietoris)Rips complex of a discrete pointset P is an abstract simplicial complex in which a subset of P defines a simplex if and only if the diameter of that subset is at most 1. We describe an efficient algorithm to determine whether a given cycle in a planar Rips complex is contractible. Our algorithm requires O(m log n) time to preprocess a set of n points in the plane in which m pairs have distance at most 1; after preprocessing, deciding whether a cycle of k Rips edges is contractible requires O(k) time. We also describe an algorithm to compute the shortest noncontractible cycle in a planar Rips complex in O(n 2 log n + mn) time.