A Distributed Algorithm to Construct Multicast Trees in WSNs: An Approximate Steiner Tree Approach

Multicast tree is a key structure for data dissemination from one source to multiple receivers in wireless networks. Minimum length multicast tree can be modeled as the Steiner Tree Problem, and is proven to be NP-hard. In this paper, we explore how to efficiently generate minimum length multicast trees in wireless sensor networks (WSNs), where only limited knowledge of network topology is available at each node. We design and analyze a simple and distributed algorithm, which we call Toward Source Tree (TST), to build multicast trees in WSNs. We show three metrics of TST algorithm, i.e., running time, tree length and energy efficiency. We prove that its running time is O(√nlog n), the best among all existing solutions to our best knowledge. We prove that TST tree length is in the same order as Steiner tree, give a theoretical upper bound and use simulations to show the ratio between them is only 1.114 when nodes are uniformly distributed. We evaluate energy efficiency in terms of the number of forwarding nodes in multicast trees, and prove that it is order-optimal. We give an efficient way to construct multicast tree in support of transmission of voluminous data.