A new approach to the design and analysis of peer-to-peer mobile networks

This paper introduces a new model and methodological approach for dealing with the probabilistic nature of mobile networks based on the theory of random graphs. Probabilistic dependence between the random links prevents the direct application of the theory of random graphs to communication networks. The new model, termed Random Network Model, generalizes conventional random graph models to allow for the inclusion of link dependencies in a mobile network. The new Random Network Model is obtained through the superposition of Kolmogorov complexity and random graph theory, making in this way random graph theory applicable to mobile networks. To the best of the authors' knowledge, it is the first application of random graphs to the field of mobile networks and a first general modeling framework for dealing with ad-hoc network mobility. The application of this methodology makes it possible to derive results with proven properties. The theory is demonstrated by addressing the issue of the establishment of a connected virtual backbone among mobile clusterheads in a peer-to-peer mobile wireless network. Using the Random Network Model, we show that it is possible to construct a randomized distributed algorithm which provides connectivity with high probability, requiring exponentially fewer connections (peer-to-peer logical links) per clusterhead than the number of connections needed for an algorithm with a worst case deterministic guarantee.