Time-Optimal Broadcasting of Multiple Messages in 1-in Port Model

Abstract

In the 1-in port model, every vertex of a synchronous network can receive each time unit at most one message. We consider simultaneous broadcasting of multiple messages from the same source in such networks with an additional restriction that every received message can be sent out to neighbors only in the next time unit and never to already informed vertex. We use a general concept of level-disjoint partitions developed for this scenario. Here we introduce a subgraph extension technique for efficient spreading information within this concept. Surprisingly, this approach with so called biwheels leads to simultaneous broadcasting of optimal number of messages on a wide class of graphs in optimal time. In particular, we provide tight results for bipartite tori, meshes, hypercubes. Several problems and conjectures are proposed.