Brief Announcement: A Fast Distributed Approximation Algorithm for Minimum Spanning Trees in the SINR Model

Abstract

We study the minimum spanning tree (MST) construction problem in wireless networks under the physical interference model based on SINR constraints. We develop the first distributed (randomized) O(μ)-approximation algorithm for MST, with the running time of O(Dlogn) (with high probability) where D denotes the diameter of the disk graph obtained by using the maximum possible transmission range, and $\mu=\log{\frac{d_{max}}{d_{min}}}$ denotes the “distance diversity” w.r.t. the largest and smallest distances between two nodes. (When $\frac{d_{max}}{d_{min}}$ is n-polynomial, μ = O(logn).)