Optimally balanced spanning tree of the star network

The one-to-all personalized broadcast problem in an interconnection network can be optimally solved with respect to both the time and the number of transmissions if it is possible to construct an optimally balanced spanning tree of the network which is also a shortest path tree. We give an algorithm to construct an optimally balanced spanning tree of the star network which is also a shortest path tree. Our result is optimal and improves on that of Chen et al. (1996) and Day and Tripathi (1994).