An O (logn) distributed approximation algorithm for local broadcasting in unstructured wireless networks

Abstract—The unstructured multi-hop radio network model, with asynchronous wake-up, no collision detection and little knowledge on the network topology, is proposed for capturing the particularly harsh characteristics of initially deployed wireless ad hoc and sensor networks. In this paper, assuming such a practical model, we study a fundamental problem of both theoretical and practical interests—the local broadcasting problem. Given a set of nodes V where each node wants to broadcast a message to all its neighbors that are within a certain local broadcasting range R, the problem is to schedule all these requests in the fewest timeslots. By adopting the physical interference model and without any knowledge on neighborhood, we give a new randomized distributed approximation algorithm for the local broadcasting problem with approximation ratio O(log n) where n is the number of nodes. This distributed approximation algorithm improves the state-of-the-art result in [22] by a logarithmic factor. I