Communication Complexity Evaluation for Longest-Lived Directional Multicasting in WANETs

We consider the problem of maximizing the multicast lifetime in wireless ad hoc networks with directional antennas. By a simulation study, we have discovered that the existing distributed algorithm for such optimization problem may generate considerable number of control messages to build up a longest-lived multicast tree in large-scale networks. This may prohibit them from being used directly in ad hoc networks with limited energy and bandwidth. In this paper, we would like to investigate some mechanisms to improve the communication complexity of the distributed algorithm. We explore some important properties of this optimization problem from a graph theory perspective and derive several localized operations that are especially beneficial to the resource-constrained (e.g. limited energy, memory, and computation capabilities) wireless ad hoc networks. The localized operations have low complexity for both memory and computation requirements at each node. Our simulation results show that the proposed localized operations would allow our distributed algorithms to achieve an expected linear communication complexity.