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4/29/2015 Wireless Sensor Networks COE 499 Deployment of Sensor Networks II Tarek Sheltami KFUPM CCSE COE 1

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2 Outline Connectivity using power control COMPOW CBTC Coverage metrics K-coverage Path observation 4/29/2015

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3 Connectivity using Power Control Once the nodes are in place transmission power settings can be used to adjust the connectivity properties of the deployed network It can extend the communication range, increasing the number of communicating neighboring nodes and improving connectivity in the form of availability of end-to-end paths. For existing neighbors, it can improve link quality (in the absence of other interfering traffic It can induce additional interference that reduces capacity and introduces congestion Some of these distributed algorithms aim to develop topologies that minimize total power consumption over routing paths, while others aim to minimize transmission power settings of each node while ensuring connectivity

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4/29/20154 Common Power Protocol The authors claim that the protocol ensures that the lowest common power level that ensures maximum network connectivity Protocol Description First multiple shortest path algorithms are performed, one at each possible power level Each node then examines the routing tables generated by the algorithm and picks the lowest power level such that the number of reachable nodes is the same as the number of nodes reachable with the maximum power level Drawbacks 1.It is not very scalable 2.By strictly enforcing common powers, it is possible that a single relatively isolated node can cause all nodes in the network to have unnecessarily large power levels

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4/29/20155 Cone-Based Topology Control Protocol The authors claim that the protocol provides a minimal direction- based distributed rule to ensure that the whole network topology is connected, while keeping the power usage of each node as small as possible. Protocol Description Each node keeps increasing its transmit power until it has at least one neighboring node in every cone or it reaches its maximum transmission power limit It is assumed here that the communication range increases monotonically with transmit power CBTC showed that suffices to ensure that the network is connected A tighter result has shown that can further reduced to

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4/29/20156 Cone-Based Topology Control Protocol Illustration of the cone-based topology control (CBTC) construction On the left an intermediate power level for a node at which there exists an cone in which the node does not have a neighbor. Therefore, as seen on the right, the node must increase its power until at least one neighbor is present in every.

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4/29/20157 Coverage Metrics The choice of coverage metric is highly dependent on the application In most networks the objective is simply to ensure that there exists a path between every pair of nodes If robustness is a concern, the K-connectivity metric may be used

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4/29/20158 K-Coverage A field is said to be K-covered if every point in the field is within the overlapping coverage region of at least K sensors. Only 2D coverage is considered in our course In an s×s unit area, with a grid of resolution unit distance, there will be such points to examine, which can be computationally intensive

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4/29/20159 K-Coverage.. A slightly more sophisticated approach would attempt to enumerate all subregions resulting from the intersection of different sensor node-regions and verify if each of these is K-covered In the worst case there can be O(n 2 ) such regions and they are not straightforward to compute

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4/29/ K-Coverage.. An area with 2-coverage (note that all intersection points are 2-covered)

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4/29/ K-Coverage..

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4/29/ Voronoi Diagrams Let S be a set of points in Euclidean space with no accumulation points. For almost any point x in the Euclidean space, there is one point of S closest to x. The word "almost" is used to indicate exceptions where a point x may be equally close to two or more points of S If S contains only two points, a and b, then the set of all points equidistant from a and b is a hyperplane—an affine subspace of codimension 1. That hyperplane is the boundary between the set of all points closer to a than to b, and the set of all points closer to b than to a In general, the set of all points closer to a point c of S than to any other point of S is the interior of a convex polytope called the Voronoi cell for c. The set of such polytopes tessellates the whole space, and is the Voronoi tessellation corresponding to the set S. If the dimension of the space is only 2, then it is easy to draw pictures of Voronoi tessellations, and in that case they are sometimes called Voronoi diagrams

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4/29/ Voronoi Diagrams..

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4/29/ Path Observation This class of coverage metrics to track targets or moving objects in sensor field Maximal Breach Distance (Voronoi Tessellation) Given a field A instrumented with sensors S where for each sensor s i ∈ S, the location (x i,y i ) is known; areas I and F corresponding to initial (I) and final (F) locations of an agent Identify P B, the Maximal Breach Path in S, starting in I and ending in F P B in this case is defined as a path through the field A, with end-points I and F and with the property that for any point p on the path P B, the distance from p to the closest sensor is maximized The regions I and F are arbitrary regions determined by the task at hand and may be located anywhere inside or outside the sensor field.

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4/29/ Path Observation Maximal Support Distance (Delaunay Triangulation) Unlike the maximal breach distance, which tries to determine the worst case observability of a traversal by a moving object Aims to provide a best-case coverage metric for moving objects Delaunay Triangulation for a set P of points in the plane is a triangulation DT(P) such that no point in P is inside the circumcircle of any triangle in DT(P).

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4/29/ Path Observation The maximal support path is the one where the moving node can stay as close as possible to sensor nodes during its traversal of the covered area Given a field A instrumented with sensors S where for each sensor s i ∈ S, the location (x i,y i ) is known; areas I and F corresponding to initial (I) and final (F) locations of an agent Identify P S, the path of Maximal support in S, starting in I and ending in F P S in this case is defined as a path through the field A, with end- points I and F and with the property that for any point p on the path P S, the distance from p to the closest sensor is minimized

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4/29/ Path Observation.. (a) maximal breach path through Voronoi cell edges (b) minimal support path through Delaunay triangulation edges

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