Minimum-Energy All-to-All Multicasting in Multi-hop Wireless Networks

Designing energy-efficient all-to-all multicasting protocols is of of great importance for multi-hop wireless networks such as wireless sensor networks and wireless ad hoc networks. In an all-to-all multicast session, there exists a set of wireless destination nodes, and each destination node needs to send some data packets to all other destination nodes. We consider the problem of building a shared multicast tree spanning the destination nodes such that the total energy consumption of realizing an all-to-all multicast session using the shared multicast tree is minimized. Since building such a multicast tree has been proved to be NP-complete, we provide both centralized and distributed approximation algorithms with provable approximation ratios for it. When the transmission power of each wireless node is fixed, our centralized and distributed algorithms have the approximation ratios of $4ln(\Delta+1)+7$ and 13, respectively, where $\Delta$ is the maximum node degree in the network. When the transmission power of each wireless node is adjustable, both of our centralized and distributed algorithms have the constant approximation ratio of 145.