Abstract
Efficiently solving the personalized broadcast problem in an interconnection network typically relies on finding an appropriate spanning tree in the network. In this paper, we show how to construct in a complete star graph an asymptotically balanced spanning tree, and in an incomplete star graph a near-balanced spanning tree. In both cases, the tree is shown to have the minimum height. In the literature, this problem has only been considered for the complete star graph, and the constructed tree is about 4/3 times taller than the one proposed in this paper.