Determining Distributions of Security Means for Wireless Sensor Networks based on the Model of a Neighbourhood Watch

Neighbourhood watch is a concept that allows a community to distribute a complex security task in between all members. Members of the community carry out individual security tasks to contribute to the overall security of it. It reduces the workload of a particular individual while securing all members and allowing them to carry out a multitude of security tasks. Wireless sensor networks (WSNs) are composed of resource-constraint independent battery driven computers as nodes communicating wirelessly. Security in WSNs is essential. Without sufficient security, an attacker is able to eavesdrop the communication, tamper monitoring results or deny critical nodes providing their service in a way to cut off larger network parts. The resource-constraint nature of sensor nodes prevents them from running full-fledged security protocols. Instead, it is necessary to assess the most significant security threats and implement specialised protocols. A neighbourhood-watch inspired distributed security scheme for WSNs has been introduced by Langend\"orfer. Its goal is to increase the variety of attacks a WSN can fend off. A framework of such complexity has to be designed in multiple steps. Here, we introduce an approach to determine distributions of security means on large-scale static homogeneous WSNs. Therefore, we model WSNs as undirected graphs in which two nodes connected iff they are in transmission range. The framework aims to partition the graph into $n$ distinct security means resulting in the targeted distribution. The underlying problems turn out to be NP hard and we attempt to solve them using linear programs (LPs). To evaluate the computability of the LPs, we generate large numbers of random {\lambda}-precision unit disk graphs (UDGs) as representation of WSNs. For this purpose, we introduce a novel {\lambda}-precision UDG generator to model WSNs with a minimal distance in between nodes.