A Deterministic and a Randomized Algorithm for Approximating Minimum Spanning Tree under the SINR Model

We describe a deterministic and a randomized distributed algorithm for computing a spanning tree over a wireless network whose weight approximates the weight of a Minimum Spanning Tree (MST). The network is composed of n static nodes embedded in a 2-dimensional Euclidean space which communicate according to the Signal-to-Interference- and-Noise Ratio (SINR) model. Under the assumption that each node knows its position and the granularity g of the network, the deterministic algorithm computes a tree within O(D log g) rounds, where D is the diameter of the graph. When nodes additionally know the local density of the network, the randomized algorithm computes a tree within O(D+log n+log g) rounds. The computed trees have weight that is within an O(log n) factor of the weight of MST. To the best of our knowledge we describe the first deterministic algorithm for this problem under the SINR model.