Optimal Broadcasting on the Star Graph

Recently the star graph has been shown as an attractive alternative to the widely used n-cube. Like the n-cube, the star graph possesses rich structure and symmetry as well as fault-tolerant capabilities, but has a smaller diameter and degree. However, very few algorithms exist to show its potential as a multiprocessor interconnection network. Many fast and efficient parallel algorithms require broadcasting as a basic step. In this paper, we propose an optimal algorithm for one-to-all broadcasting in the star graph. The algorithm can broadcast a message to N processors in O(log₂N) time. The algorithm exploits the rich structure of the star graph and works by recursively partitioning the original star graph into smaller star graphs. In addition, we develop an optimal all-to-all broadcasting algorithm.