Throughput-Optimal Broadcast in Wireless Networks with Point-to-Multipoint Transmissions

TLDR: The NP-completeness of the finite-horizon broadcasting problem is proved, which is in contrast with the polynomial-time solvability of the problem with point-to-point channels.

Abstract: We consider the problem of efficient packet dissemination in wireless networks with point-to-multipoint wireless broadcast channels. We propose a dynamic policy, which achieves the broadcast capacity of the network. This policy is obtained by first transforming the original multi-hop network into a precedence-relaxed virtual single-hop network and then finding an optimal broadcasting policy for the relaxed network. The resulting policy is shown to be throughput-optimal for the original wireless network using a sample-path argument. We also prove the NP -completeness of the finite-horizon broadcasting problem, which is in contrast with the polynomial-time solvability of the problem with point-to-point channels. Illustrative simulation results demonstrate the efficacy of the proposed broadcast policy in achieving the full broadcast capacity with low delay.