Practical Random Tree Generation: Information-Theoretic Analysis and Applications to IoT

Tree structures make an appearance in many network related problems, such as network routing. Modelling and simulating the appearance of these data structures can be done using random tree generators. However, there has been very little study on random models that are able to capture the dynamics of networks. We introduce the random spanning tree model, which is a random tree generator that is based on generating a tree from an already existing network topology. The Shannon entropy of this model is then analysed, and upper bounds to it are found. As compression can be beneficial because of the complexity of large trees, we then introduce a universal approach to compressing trees generated using the spanning tree model. It will be shown that the proposed method of compression introduces a redundancy that tends to zero for larger trees. We recommend the use of this random model and the proposed compression algorithm in routing protocols of IoT, as it can contribute to saving routing communication overhead and increasing the overall lifetime of the network.