True ConvergeCast Scheduling in Wireless Sensor Networks

An important application of Wireless Sensor Networks (WSNs) is target monitoring: sensors monitor a set of targets, and forward the collected data using multi-hop routing to the same location, called the sink. The resulting communication pattern is called ConvergeCast. Several researchers studied the problem of assigning TDMA time slots in order to minimize data collection time using mathematical programming models, with the claim that those models provide an optimal or a near-optimal ConvergeCast schedule. However, those models only output a multi-set of so-called transmission configurations, i.e., sets of links that can simultaneously transmit, and which together cover the links in all paths from sensors to the sink. In particular, these models do not provide an ordering of the transmission configurations, nor do they guarantee that such an ordering exists using no more than the minimum number of slots their model outputs. In this paper, we give for the first time, a mathematical programming formulation for a complete and optimal solution, i.e., an ordered sequence of transmission configurations that achieves ConvergeCast. This solution provides much better results than heuristic approaches in the literature, and a "true" scheduling in comparison with the previous mathematical programming approaches.