Distributed Computing in Fault-Prone Dynamic Networks

Dynamics in networks is caused by a variety of reasons, like nodes moving in 2D (or 3D) in multihop cellphone networks, joins and leaves in peer-to-peer networks, evolution in social networks, and many others. In order to understand such kinds of dynamics, and to design distributed algorithms that behave well under dynamics, many ways to model dynamics are introduced and analyzed w.r.t. correctness and eciency of distributed algorithms. In [16], Kuhn, Lynch, and Oshman have introduced a very general, worst case type model of dynamics: The edge set of the network may change arbitrarily from step to step, the only restriction is that it is connected at all times and the set of nodes does not change. An extended model demands that a xed connected subnetwork is maintained over each time interval of length T (T-interval dynamics). They have presented, among others, algorithms for counting the number of nodes under such general models of dynamics.In this paper, we generalize their models and algorithms by adding random edge faults, i.e., we consider fault-prone dynamic networks: We assume that an edge currently existing may fail to transmit data with some probability p. We rst observe that strong counting, i.e., each node knows the correct count and stops, is not possible in a model with random edge faults. Our main two positive results are feasibility and runtime bounds for weak counting, i.e., stopping is no longer required (but still a correct count in each node), and for strong counting with an upper bound, i.e., an upper bound N on n is known to all nodes.