Extremal properties of three-dimensional sensor networks with applications

Abstract

In this paper, we analyze various critical transmitting/sensing ranges for connectivity and coverage in three-dimensional sensor networks. As in other large-scale complex systems, many global parameters of sensor networks undergo phase transitions: For a given property of the network, there is a critical threshold, corresponding to the minimum amount of the communication effort or power expenditure by individual nodes, above (resp. below) which the property exists with high (resp. a low) probability.For sensor networks, properties of interest include simple and multiple degrees of connectivity/coverage. First, we investigate the network topology according to the region of deployment, the number of deployed sensors and their transmitting/sensing ranges. More specifically, we consider the following problems:Assume that n nodes, each capable of sensing events within a radius of r, are randomly and uniformly distributed in a 3-dimensional region R of volume V , how large must the sensing range r Sense be to ensure a given degree of coverage of the region to monitor? For a given transmission range r Trans , what is the minimum (resp. maximum) degree of the network? What is then the typical hop-diameter of the underlying network? Next, we show how these results affect algorithmic aspects of the network by designing specific distributed protocols for sensor networks.

Sixsoid: A new paradigm for k-coverage in 3D wireless sensor networks

“…Prior to that the following works disscuss the 3D version; in [16], authors propose a coverage optimization algorithm based on sampling for 3D underwater WSNs. [12] proposes an optimal polynomial time algorithm based on voronoi diagram and graph search algorithms, in [9] authors suggest algorithms to ensure k-coverage of every point in a field where sensors may have same or different sensing radii, [10] defines the minimum number of sensors for kcoverage with a probability value, [15] studies the effect of sensing radius on the probability of k-coverage, [7] proposes an optimal deployment strategy to deal with full coverage and 2-connectivity, [4] brought forward a sensor placement model based on Voronoi structure to cover a 3D region, in [14], authors provide a study on connectivity and coverage issues in a randomly deployed 3D WSN. In this paper, we compare our proposed Sixsoid based k-coverage model with the existing Reuleaux Tetrahedron based model [1].…”

Actor positioning based on molecular geometry in aerial sensor networks

“…This problem turns into the sphere packing problem in three dimensions. Ravelomanana [2] studies the properties of network topologies that result from random deployment of nodes in a 3D region of interest to provide theoretical bounds. The author derives conditions for the node transmission range r required for achieving a degree of connectivity d, where every node has at least d neighbors.…”

Routing algorithms for delay-insensitive and delay-sensitive applications in underwater sensor networks

“…The depth of the sensor can then be regulated by adjusting the length of the wire that connects the sensor to the anchor, by means of an electronically controlled engine that resides on the sensor. Sensor should coordinate their depths in such a way as to guarantee that the network topology be always connected, i.e., at least one path from every sensor to the surface station always exists, and achieve communication coverage [22], as further discussed in [4]. Although AUVs can add a remarkable degree of flexibility to the network architecture, they also introduce new important challenges due to their mobility.…”

“…represents the packet error rate, given the packet size LP , the FEC redundancy L F P , and the bit error rate (BER), and it depends on the adopted FEC technique F. • P ER e2e max is the application maximum allowed end-to-end packet error rate, while N Hop max is the maximum expected number of hops, function of the network diameter [22].…”