A topological model for wireless sensor networks

Jan Terzer (2016) A topological model for wireless sensor networks. EngD thesis.

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Abstract

Sensors are devices for extracting information from the environment. In order to cover a larger area of detection, they are spread across the desired domain and connected in a sensor network. The question arises whether the sensors cover the entire area of domain or in other words whether there is an area within the domain that sensors do not detect. An area such as this is called a hole. In wireless non-stationary sensor networks the location of the individual sensors is not known, only information on which sensors are connected is available. The coverage of the domain of such a sensor network can be determined using topological methods. Using information on connectivity between the sensors we build the Rips complex and compute its homology groups and Betti numbers. The thesis presents a simulator for generating sensor networks and calculating the number of holes in it by computing the first Betti number of the corresponding Rips complex.

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