  Given the increasing demand from wireless applications, designing
energy-efficient group communication protocols is of great importance to
multi-hop wireless networks. A group communication session involves a set of
member nodes, each of them needs to send a certain number of data packets to
all other members. In this paper, we consider the problem of building a shared
multicast tree spanning the member nodes such that the total energy consumption
of a group communication session using the shared multicast tree is minimized.
Since this problem was proven as NP-complete, we propose, under our Min-Energy
Group COMmunication (MEGCOM) framework, three distributed approximation
algorithms with provable approximation ratios. When the transmission power of
each wireless node is fixed, our first two algorithms have the approximation
ratios of O(ln(\Delta+ 1)) and O(1), respectively, where \Delta is the maximum
node degree in the network. When the transmission power of each wireless node
is adjustable, our third algorithm again delivers a constant approximation
ratio. We also use extensive simulations to verify the practical performance of
our algorithms.
