Efficient multicast trees with local knowledge on wireless ad hoc networks

In this paper we address the problem of establishing a cost efficient multicast tree among a group of stationary nodes in a multi-hop wireless network. The flooding of broadcast discovery messages is a major limitation to the scalability of most ad hoc protocols. To avoid massive flooding, we limit the reach of broadcast discovery messages, and consider the case were joining nodes can only learn limited information about the multicast group topology from neighbors within a fixed number of hops. We propose two algorithms that satisfy this constraint. We analyze the worst case cost of the established trees and prove that the first algorithm builds a minimal cost spanning tree, while the second builds a sub-optimal tree with a worst-case approximation ratio of O(log n/loglog n). The advantage of the second algorithm is that the communication requirement for a node to join the multicast tree is smaller. We simulate and compare the proposed algorithms. Finally, we discuss the implementation issues and scenarios for using each one of them. We also describe our secure multicast application that builds on top of the proposed protocols.