We consider the local broadcasting problem in the SINR model, which is a basic primitive for gathering initial information among @math wireless nodes. Assuming that nodes can measure received power, we achieve an essentially optimal constant approximate algorithm (with a @math additive term). This improves upon the previous best @math -approximate algorithm. Without power measurement, our algorithm achieves @math -approximation, matching the previous best result, but with a simpler approach that works under harsher conditions, such as arbitrary node failures. We give complementary lower bounds under reasonable assumptions.
@cite_19: 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 adhoc 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 mode land 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 nis the number of nodes. This distributed approximation algorithm improves the state-of-the-art result in [22] by a logarithmic factor.
@cite_1: 
@cite_17: Given a set of sensor nodes V where each node wants to broadcast a message to all its neighbors that are within a certain broadcasting range, the local broadcasting problem is to schedule all these requests in as few timeslots as possible. In this paper, assuming the more realistic physical interference model and no knowledge of the topology, we present three distributed local broadcasting algorithms where the first one is for the asynchronized model and the other two are for the synchronized model. Under the asynchronized model, nodes may join the execution of the protocol at any time and do not have access to a global clock, for which we give a distributed randomized algorithm with approximation ratio O(log2 n). This improves the state-of-the-art result given in [14] by a logarithmic factor. For the synchronized model where communications among nodes are synchronous and nodes can perform physical carrier sensing, we propose two distributed deterministic local broadcasting algorithms for synchronous and asynchronous node wakeups, respectively. Both algorithms have approximation ratio O(log n).
The bounds for unknown competition were improved in @cite_17 to @math , optimizing the algorithm of @cite_1 . Additionally, @math -approximate deterministic algorithms were given for a synchronized model where a carrier-sense primitive was assumed to be available. Finally, an @math -approximate randomized algorithm without a carrier-sense primitive was very recently proposed in @cite_19 . A lower bound of @math was also given.