Communication in Networks with Random Dependent Faults

Abstract

The aim of this paper is to study communication in networks where nodes fail in a random dependent way. In order to capture fault dependencies, we introduce the neighborhood fault model, where damaging events, called spots, occur randomly and independently with probability p at nodes of a network, and cause faults in the given node and all of its neighbors. Faults at distance at most 2 become dependent in this model and are positively correlated. We investigate the impact of spot probability on feasibility and time of communication in the fault-free part of the network. We show a network which supports fast communication with high probability, if p ≤ 1/clogn. We also show that communication is not feasible with high probability in most classes of networks, for constant spot probabilities. For smaller spot probabilities, high probability communication is supported even by bounded degree networks. It is shown that the torus supports communication with high probability when p decreases faster than 1/n ^1/2, and does not when p ∈ 1/O(n ^1/2). Furthermore, a network built of tori is designed, with the same fault-tolerance properties and additionally supporting fast communication. We show, however, that networks of degree bounded by a constant d do not support communication with high probability, if p ∈ 1/O(n ^1/d). While communication in networks with independent faults was widely studied, this is the first analytic paper which investigates network communication for random dependent faults.