Distributed backbone structure for algorithms in the SINR model of wireless networks

The Signal-to-Interference-and-Noise-Ratio (SINR) physical model is one of the most popular models of wireless networks. Despite of the vast amount of study done in design and analysis of centralized algorithms supporting wireless communication under the SINR physical model, little is known about distributed algorithms in this model, especially deterministic ones. In this work we construct, in a deterministic distributed way, a backbone structure on the top of a given wireless network, which can be used for efficient transformation of many algorithms designed in a simpler model of ad hoc broadcast networks without interference into the SINR physical model with uniform power of stations. The time cost of the backbone data structure construction is only O(Δ polylog N) rounds, where Δ is roughly the network density and {1,...,N} is the range of identifiers (IDs) and thus N is an upper bound on the number of nodes in the whole network. The core of the construction is a novel combinatorial structure called SINR-selector, which is introduced in this paper. We demonstrate the power of the backbone data structure by using it for obtaining efficient O(D + Δ polylog N) round and O(D + k + Δ polylog N) round deterministic distributed solutions for leader election and multi-broadcast, respectively, where D is the network diameter and k is the number of messages to be disseminated.