This paper considers the problem of how to efficiently share a wireless medium which is subject to harsh external interference or even jamming. While this problem has already been studied intensively for simplistic single-hop or unit disk graph models, we make a leap forward and study MAC protocols for the SINR interference model (a.k.a. the physical model). We make two contributions. First, we introduce a new adversarial SINR model which captures a wide range of interference phenomena. Concretely, we consider a powerful, adaptive adversary which can jam nodes at arbitrary times and which is only limited by some energy budget. The second contribution of this paper is a distributed MAC protocol which provably achieves a constant competitive throughput in this environment: we show that, with high probability, the protocol ensures that a constant fraction of the non-blocked time periods is used for successful transmissions. Our results also highlight an inherent difference between the SINR model and unit disk graph models.

Epidemic processes are widely used to design efficient distributed algorithms with applications in various research fields. In this paper, we consider a dynamic epidemic process in a certain (idealistic) urban environment modeled by a complete graph. The epidemic is spread among $n$ agents, which move from one node to another according to a power law distribution that describes the so called attractiveness of the corresponding locations in the urban environment. If two agents meet at some node, then a possible infection may be transmitted from one agent to the other.