3-Dimensional minimum energy broadcasting problem

The minimum energy broadcast routing problem was extensively studied during the last years. Given a sample space where wireless devices are distributed, the aim is to perform the broadcast communication pattern from a given source while minimising the total energy consumption. While many papers deal with the 2-dimensional case where the sample space is given by a plain area, few results are known about the more interesting and practical 3-dimensional case. In this paper we study this case and we present a tighter analysis of the minimum spanning tree heuristic in order to considerably decrease its approximation factor from the known 26 to roughly 18.8. This decreases the gap with the known lower bound of 12 given by the so-called 3-dimensional kissing number.