Optimal Multicast Scheduling for Millimeter Wave Networks Leveraging Directionality and Reflections

We investigate the minimum-delay multicast problem for millimeter wave (mmWave) networks. Salient characteristics of mmWave links, directionality and reflections, are considered under sectored antenna model. We first consider directionality only, and identify the property such that the optimal policy can be recursively partitioned into smaller sizes. Using such optimal substructure, we propose an iterative method based on graphs which finds the optimal schedule in polynomial time. Next, we extend our model to incorporate reflections. We introduce the concept of path diversity which states that the availability of reflected paths enables opportunistic reduction of multicast delay. We prove NP-hardness of the problem, and propose approximations with performance bounds and heuristics of reduced complexity. By simulation we show the outperformance of our method over conventional ones, and numerically characterize the gain of path diversity in terms of network size.