Determining Distributions of Security Means for WSNs based on the Model of a Neighbourhood Watch

TL;DR

This work addresses distributing multiple security means across large-scale static WSNs by modeling the network as a graph and seeking static, near-optimal partitions into $n$ disjoint dominating sets via $0$-$1$ linear programs (LPs). It introduces the concept of $n$-soft domatic partitions to handle cases where a full $n$-domatic partition may not exist and provides two LP formulations—one for optimal and one for maximal partitions—augmented with resource-cost and auxiliary-variable approaches. A novel $\\lambda$-precision UDG generator is developed to generate large, controllable WSN graphs for empirical evaluation, with tunable coverage and degree properties. Empirical results demonstrate the computability and quality trade-offs of the proposed partitions on up to 300-node graphs, highlighting that optimal partitions reduce missing coverages more than maximal ones while maintaining comparable incompletely covered nodes. The methods are positioned to support design-space exploration of cooperative security configurations in WSNs and could inform practical deployment strategies such as defense-in-depth schemes in forest monitoring scenarios.

Abstract

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 Langendörfer. 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 λ-precision unit disk graphs (UDGs) as representation of WSNs. For this purpose, we introduce a novel λ-precision UDG generator to model WSNs with a minimal distance in between nodes.

Figures (9)

• Figure 1: The set of green nodes is a dominating set in the given graph.
• Figure 2: The example shows a graph in which the nodes are mapped to a domatic partition consisting of three dominating sets.
• Figure 3: The partition of the graph is not a domatic partition because there exist nodes in at least one dominating set of the partition that has no neighbourship with at least one node of each of the other dominating sets of the partition.
• Figure 4: As example for the resulting $\lambda$-precision UDGs shown per row are from left to right generated for $A_\text{coverage}$ of the ranges $[0.850,0.875]$, $[0.900,0.925]$, $[0.925,0.950]$ and $[0.975,1.000]$ respectively.
• Figure 5: The mean of the variance of the local cluster coefficients tends to decrease along with increasing $\overline{A_\text{coverage}}$ leading to more homogeneously distributed nodes with larger pairwise distances. A sample size of $40$ graphs per data point has been utilised. This sample size balances the expressivity of the decrease trend with the computational effort for parameterised graph generation.