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Evasion paths in mobile sensor networks
, 2013
"... Suppose that ballshaped sensors wander in a bounded domain. A sensor doesn’t know its location but does know when it overlaps a nearby sensor. We say that an evasion path exists in this sensor network if a moving intruder can avoid detection. In Coordinatefree coverage in sensor networks with cont ..."
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Suppose that ballshaped sensors wander in a bounded domain. A sensor doesn’t know its location but does know when it overlaps a nearby sensor. We say that an evasion path exists in this sensor network if a moving intruder can avoid detection. In Coordinatefree coverage in sensor networks with controlled boundaries via homology, Vin de Silva and Robert Ghrist give a necessary condition, depending only on the timevarying connectivity data of the sensors, for an evasion path to exist. Using zigzag persistent homology, we provide an equivalent condition that moreover can be computed in a streaming fashion. However, no method with timevarying connectivity data as input can give necessary and sufficient conditions for the existence of an evasion path. Indeed, we show that the existence of an evasion path depends not only on the fibrewise homotopy type of the region covered by sensors but also on its embedding in spacetime. For planar sensors that also measure weak rotation and distance information, we provide necessary and sufficient conditions for the existence of an evasion path. 1
Realistic, Efficient and Secure Geographic Routing in Vehicular Networks
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Connectivity in TwoDimensional Lattice Networks
"... Abstract—Connectivity has been extensively studied in ad hoc networks, most recently with the application of percolation theory in twodimensional square lattices. Given a message source and the bond probability to connect neighbor vertexes on the lattice, percolation theory tries to determine the c ..."
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Abstract—Connectivity has been extensively studied in ad hoc networks, most recently with the application of percolation theory in twodimensional square lattices. Given a message source and the bond probability to connect neighbor vertexes on the lattice, percolation theory tries to determine the critical bond probability above which there exists an infinite connected giant component with high probability. This paper studies a related but different problem: what is the connectivity from the source to any vertex on the square lattice following certain directions? The original directed percolation problem has been studied in statistical physics for more than half a century, with only simulation results available. In this paper, by using a recursive decomposition approach, we have obtained the analytical expressions for directed connectivity. The results can be widely used in wireless and mobile ad hoc networks, including vehicular ad hoc networks. Index Terms—Connectivity, square lattice, directed percolation I.
A New Approach to the Directed Connectivity in TwoDimensional Lattice Networks
"... Abstract—The connectivity of ad hoc networks has been extensively studied in the literature. Most recently, researchers model ad hoc networks with twodimensional lattices and apply percolation theory for connectivity study. On the lattice, given a message source and the bond probability to connect ..."
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Abstract—The connectivity of ad hoc networks has been extensively studied in the literature. Most recently, researchers model ad hoc networks with twodimensional lattices and apply percolation theory for connectivity study. On the lattice, given a message source and the bond probability to connect any two neighbor vertices, percolation theory tries to determine the critical bond probability above which a giant connected component appears. This paper studies a related but different problem, directed connectivity: what is the exact probability of the connection from the source to any vertex following certain directions? The existing studies in math and physics only provide approximation or numerical results. In this paper, by proposing a recursive decomposition approach, we can obtain a closedform polynomial expression of the directed connectivity of square lattice networks as a function of the bond probability. Based on the exact expression, we have explored the impacts of the bond probability and lattice size and ratio on the lattice connectivity, and determined the complexity of our algorithm. Further, we have studied a realistic ad hoc network scenario, i.e., an urban VANET, where we show the capability of our approach on both homogeneous and heterogeneous lattices and how related applications can benefit from our results. Index Terms—Connectivity, square lattices, bond percolation, ad hoc networks F 1
Geometric Methods of Information Storage and Retrieval in Sensor Networks
, 2013
"... Sensor networks collect data from their environment. Locations of the sensors are important attributes of that information and provide a context to understand, and use sensor data. In this chapter, we will discuss geometric ideas to organize sensor data using their locations. We will consider distri ..."
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Sensor networks collect data from their environment. Locations of the sensors are important attributes of that information and provide a context to understand, and use sensor data. In this chapter, we will discuss geometric ideas to organize sensor data using their locations. We will consider distributed methods for managing queries about isolated events, queries about mobile objects, and queries for general signal fields. Location based methods often operate on simple geometric domains, and we will discuss how they can be adapted to networks with complex shapes. 1