Homology-based Distributed Coverage Hole Detection in Wireless Sensor Networks

Homology theory provides new and powerful solutions to address the coverage problems in wireless sensor networks (WSNs). They are based on algebraic objects, such as Cech complex and Rips complex. Cech complex gives accurate information about coverage quality but requires a precise knowledge of the relative locations of nodes. This assumption is rather strong and hard to implement in practical deployments. Rips complex provides an approximation of Cech complex. It is easier to build and does not require any knowledge of nodes location. This simplicity is at the expense of accuracy. Rips complex can not always detect all coverage holes. It is then necessary to evaluate its accuracy. This work proposes to use the proportion of the area of undiscovered coverage holes as performance criteria. Investigations show that it depends on the ratio between communication and sensing radii of a sensor. Closed-form expressions for lower and upper bounds of the accuracy are also derived. For those coverage holes which can be discovered by Rips complex, a homology-based distributed algorithm is proposed to detect them. Simulation results are consistent with the proposed analytical lower bound, with a maximum difference of 0.5%. Upper bound performance depends on the ratio of communication and sensing radii. Simulations also show that the algorithm can localize about 99% coverage holes in about 99% cases

Construction of the generalized Cech complex

In this paper, we introduce an algorithm which constructs the generalized Cech complex. The generalized Cech complex represents the topology of a wireless network whose cells are different in size. This complex is often used in many application to locate the boundary holes or to save energy consumption in wireless networks. The complexity of a construction of the Cech complex to analyze the coverage structure is found to be a polynomial time

A note on the simulation of the Ginibre point process

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Stochastic Geometry: Boolean model and random geometric graphs

International audienceThis paper collects the four contributions which were presented during the session devoted to Stochastic Geometry at the journées MAS 2014. It is focused in particular on several questions related to the transmission of information in a general sense in different random media. The underlying models include the Boolean model, simplicial complexes or geometric random graphs induced by a point process

Evidence of interseismic coupling variations along the Bhutan Himalayan arc from new GPS data

Although the first-order pattern of present-day deformation is relatively well resolved across the Himalayas, irregular data coverage limits detailed analyses of spatial variations of interseismic coupling. We provide the first GPS velocity field for the Bhutan Himalaya. Combined with published data, these observations show strong east-west variations in coupling between central and eastern Bhutan. In contrast with previous estimations of first-order uniform interseismic coupling along the Himalayan arc, we identify significant lateral variations: In western and central Bhutan, the fully coupled segment is 135-155km wide with an abrupt downdip transition, whereas in eastern Bhutan the fully coupled segment is 100-120km wide and is limited updip and downdip by partially creeping segments. This is the first observation of decoupling on the upper ramp along the Himalayan arc, with important implications for large earthquake surface rupture and seismic hazard