Broadcast Schemes of Hypercubes

Abstract

Broadcasting is a fundamental process in network communication, modeled as the dissemination of information across vertices in a graph. This paper investigates the broadcast problem in hypercube graphs and revisits the dimensional broadcast schemes. We propose a novel algorithm that generates all valid minimum-time broadcast schemes by using the recursive structure of hypercubes. Additionally, we compute the total number of valid minimum-time broadcast schemes in hypercubes, which is also the number of all spanning binomial trees. We also give an enumeration of all valid minimum-time broadcast schemes.