What are some applications of computational geometry in wireless sensor networks?

2 Coverage problems

One of the fundamental problems in WSNs is to determine how well the sensor nodes cover the region of interest. Coverage can be defined in different ways, depending on the application and the sensing model. For example, a WSN may aim to achieve full coverage, where every point in the region is within the sensing range of at least one sensor node, or barrier coverage, where there is no path across the region that avoids the sensing range of all sensor nodes. Computational geometry can help to solve coverage problems by providing efficient algorithms for computing and optimizing the coverage area, the overlap area, the boundary area, and the holes or gaps in the coverage. Some of the geometric techniques that can be used for coverage problems include Voronoi diagrams, Delaunay triangulations, convex hulls, and disk packing.

3 Connectivity problems

Another important problem in WSNs is to ensure that the sensor nodes can communicate with each other and with the base station. Connectivity can be affected by the network topology, the communication range, the interference, and the node failures. Computational geometry can help to solve connectivity problems by providing efficient algorithms for computing and optimizing the network graph, the shortest paths, the spanning trees, the routing protocols, and the network partitions. Some of the geometric techniques that can be used for connectivity problems include geometric graphs, visibility graphs, proximity graphs, and geometric spanners.

4 Lifetime problems

A third major problem in WSNs is to prolong the network lifetime, which is the time until the network fails to perform its function due to the depletion of the sensor nodes' batteries. Lifetime can be improved by reducing the energy consumption of the sensor nodes, which depends on the sensing, processing, and communication activities. Computational geometry can help to solve lifetime problems by providing efficient algorithms for computing and optimizing the energy consumption, the energy balance, the energy harvesting, and the energy replenishment. Some of the geometric techniques that can be used for lifetime problems include network decomposition, network clustering, network scheduling, and network reconfiguration.