Minimum gossip bus networks

Abstract

Gossiping is an information dissemination problem in which each node of a communication network has a unique piece of information that must be transmitted to all the other nodes. A bus network is a network of processing elements that communicate by sending messages along buses in a sequence of calls. We assume that (i) each node can participate in at most one call at a time, (ii) a node can either send or receive on/ from a bus (exclusively), (iii) no more than one node can send a message on a given bus at a given time, and (iv) communicating a message on a bus takes a unit of time. This model extends the telegraph model in allowing the number of nodes connected to each bus to be as large as needed, instead of being bounded by 2. In this paper, we are interested in minimizing the hardware of a bus network in keeping optimal the communication performances for solving the gossiping problem. More precisely, we compute the minimum number of buses required for gossiping to be optimal. Similarly, we give upper bounds on the minimum length of buses required for gossiping to be optimal. Finally, we combine the two approaches in trying to minimize both parameters: length and number of buses.