On the Broadcast problem for mobile agents in dynamic networks

Abstract

We study the standard communication problem of broadcast for mobile agents moving in a network, where a single agent called source, has to transmit a vital information to all other agents in the network. The agents move autonomously in the network and can communicate with other agents only when they meet at a node. Previous studies of this problem were restricted to static networks while, in this paper, we consider the problem in dynamic networks modeled as an evolving graph. The dynamicity of the graph is unknown to the agents; in each round an adversary selects which edges of the graph are available, and an agent can choose to traverse one of the available edges adjacent to its current location. The only restriction on the adversary is that the subgraph of available edges in each round must span all nodes; in other words the evolving graph is constantly connected. The agents have global visibility allowing them to see the location of all agents in the graph and move accordingly. Depending on the topology of the underlying graph, we determine the minimum value of $k>0$, such that the broadcast from a source agent to $k$ other agents can be solved in dynamic networks. While $k=2$ agents are sufficient for ring networks, much larger teams of agents are necessary for denser graphs such as grid graphs and hypercubes, and finally for complete graphs of $n$ nodes $k\ge n-2$ agents are necessary and sufficient. We show lower bounds on the number of agents and provide algorithms for solving broadcast using the minimum number of agents, for various topologies. These results show how the connectivity of the underlying graph affects the communication capability of a team of mobile agents in constantly connected dynamic networks.