A distributed algorithm to construct multicast trees in wireless multi-hop networks

The minimum-length multicast tree can achieve efficient multicast transmissions and can be formulated as a Steiner Tree. Its construction is non-trivial and has been proven to be NP-hard. In this paper, we combine the design wisdoms in the minimum spanning tree and the shortest path, and propose a new distributed algorithm for constructing an approximate Steiner Tree, particularly applicable to dynamic wireless networks without centralized control. We rigorously prove the performance bounds of our algorithm in terms of tree length, running time and energy consumption. Let m be the multicast group size and n be the network size. We theoretically show that the ratio of our tree length to the minimum value is upper bounded by equation (where δ can be any positive value). Simulation results show that this ratio is in fact very close to 1. We also prove that the running time is equation. The energy consumption is evaluated in terms of message complexity, and is upper bounded by O(n logm). In all, our algorithm achieves the near-optimal tree length, as well as the shortest running time and the lowest message complexity among all solutions we are aware of. We believe our algorithm provides a significant improvement in designing practical routing policies in wireless networks.