Delaunay Triangulation as a New Coverage Measurement Method in Wireless Sensor Network

Sensing and communication coverage are among the most important trade-offs in Wireless Sensor Network (WSN) design. A minimum bound of sensing coverage is vital in scheduling, target tracking and redeployment phases, as well as providing communication coverage. Some methods measure the coverage as a percentage value, but detailed information has been missing. Two scenarios with equal coverage percentage may not have the same Quality of Coverage (QoC). In this paper, we propose a new coverage measurement method using Delaunay Triangulation (DT). This can provide the value for all coverage measurement tools. Moreover, it categorizes sensors as ‘fat’, ‘healthy’ or ‘thin’ to show the dense, optimal and scattered areas. It can also yield the largest empty area of sensors in the field. Simulation results show that the proposed DT method can achieve accurate coverage information, and provides many tools to compare QoC between different scenarios

The localized Delaunay triangulation and ad-hoc routing in heterogeneous environments

Ad-Hoc Wireless routing has become an important area of research in the last few years due to the massive increase in wireless devices. Computational Geometry is relevant in attempts to build stable, low power routing schemes. It is only recently, however, that models have been expanded to consider devices with a non-uniform broadcast range, and few properties are known. In particular, we find, via both theoretical and experimental methods, extremal properties for the Localized Delaunay Triangulation over the Mutual Inclusion Graph. We also provide a distributed, sub-quadratic algorithm for the generation of the structure

Probabilistic Bounds on the Length of a Longest Edge in Delaunay Graphs of Random Points in d-Dimensions

Motivated by low energy consumption in geographic routing in wireless networks, there has been recent interest in determining bounds on the length of edges in the Delaunay graph of randomly distributed points. Asymptotic results are known for random networks in planar domains. In this paper, we obtain upper and lower bounds that hold with parametric probability in any dimension, for points distributed uniformly at random in domains with and without boundary. The results obtained are asymptotically tight for all relevant values of such probability and constant number of dimensions, and show that the overhead produced by boundary nodes in the plane holds also for higher dimensions. To our knowledge, this is the first comprehensive study on the lengths of long edges in Delaunay graphsComment: 10 pages. 2 figures. In Proceedings of the 23rd Canadian Conference on Computational Geometry (CCCG 2011). Replacement of version 1106.4927, reference [5] adde

On Geometric Spanners of Euclidean and Unit Disk Graphs

We consider the problem of constructing bounded-degree planar geometric spanners of Euclidean and unit-disk graphs. It is well known that the Delaunay subgraph is a planar geometric spanner with stretch factor C_{del\approx 2.42; however, its degree may not be bounded. Our first result is a very simple linear time algorithm for constructing a subgraph of the Delaunay graph with stretch factor \rho =1+2\pi(k\cos{\frac{\pi{k)^{-1 and degree bounded by $k$, for any integer parameter $k\geq 14$. This result immediately implies an algorithm for constructing a planar geometric spanner of a Euclidean graph with stretch factor \rho \cdot C_{del and degree bounded by $k$, for any integer parameter $k\geq 14$. Moreover, the resulting spanner contains a Euclidean Minimum Spanning Tree (EMST) as a subgraph. Our second contribution lies in developing the structural results necessary to transfer our analysis and algorithm from Euclidean graphs to unit disk graphs, the usual model for wireless ad-hoc networks. We obtain a very simple distributed, {\em strictly-localized algorithm that, given a unit disk graph embedded in the plane, constructs a geometric spanner with the above stretch factor and degree bound, and also containing an EMST as a subgraph. The obtained results dramatically improve the previous results in all aspects, as shown in the paper

A clustered back-bone for routing in ad-hoc networks

In the recent years, a lot of research work has been undertaken in the area of ad-hoc networks due to the increasing potential of putting them to commercial use in various types of mobile computing devices. Topology control in ad-hoc networks is a widely researched topic; with a number of algorithms being proposed for the construction of a power-efficient topology that optimizes the battery usage of the mobile nodes. This research proposes a novel technique of partitioning the ad-hoc network into virtually-disjoint clusters. The ultimate aim of forming a routing graph over which power-efficient routing can be implemented in a simple and effective manner is realized by partitioning the network into disjoint clusters and thereafter joining them through gateways to form a connected, planar back-bone which is also a t-spanner of the original Unit Disk Graph (UDG). Some of the previously proposed algorithms require the nodes to construct local variations of the Delaunay Triangulation and undertake several complicated steps for ensuring the planarity of the back-bone graph. The construction of the Delaunay Triangulation is very complex and time-consuming. This work achieves the objective of constructing a routing graph which is a planar spanner, without requiring the expensive construction of the Delaunay Triangulation, thus saving the node power, an important resource in the ad-hoc network. Moreover, the algorithm guarantees that the total number of messages required to be sent by each node is O(n). This makes the topology easily reconfigurable in case of node motion