Minimum Energy Multicast Routing for Wireless Ad-hoc Networks with Adaptive Antennas Song Guo and Oliver Yang School of Information and Technology, University of Ottawa Ottawa, Ontario, Canada, K1N 6N5 {sguo, yang}@site.uottawa.ca Abstract Energy conservation is a critical issue in wireless multihop ad-hoc networks, which have nodes powered by batteries only. One major metric for energy conservation is to route a communication session along the routes that require the lowest total energy consumption. In this paper, we consider wireless ad hoc networks that use adaptive antennas and have limited energy resources. To explore the advantages of power saving offered by the use of adaptive antennas, we consider the case of source initiated multicast traffic. We present a constraint formulation for the MEM (Minimum-Energy Multicast) problem in terms of MILP (Mixed Integer Linear Programming) for wireless ad hoc networks. Experiment results show that an optimal solution of the MEM problem using our MILP model can always be obtained in a timely manner for moderately sized network, and it also provides a way to evaluate the realistic performance of different heuristic algorithms. 1. Introduction An ad hoc network is a peer-to-peer mobile network consisting of large number of mobile nodes. These nodes create an instant network on demand and may communicate with each other via intermediate nodes in a multi-hop mode, i.e., every node can be a router. Ad hoc networks may be the only solution in many situations where instant infrastructure is needed and no central backbone system and administration (like base stations and wired backbone in a cellular system) exist. Some of the applications include mobile computing in areas where other infrastructure is unavailable, law enforcement operations, as well as disaster recovery situations. Each node in such a network has a limited energy resource (battery), and each node operates in an unattended manner. Consequently, energy efficiency is an important design consideration for these networks. In this paper, we explore the energy conservation offered by the use of directional antennas for broadcasting /multicasting in wireless ad hoc networks. The broadcast/multicast communication is an important mechanism to communicate information in wireless ad hoc networks. This is because the network described above can be regarded as a distributed system, where broadcast /multicast is an important communication primitive. In addition, many routing protocols for wireless ad-hoc networks need a broadcast /multicast mechanism to update their states and maintain the routes between nodes. When power efficiency is considered, ad hoc networks will require a power-aware metric for their routing algorithms. Typically, there are two main optimization metrics for energy-efficiency broadcast/ multicast routing in wireless ad hoc networks: (1) Maximizing the network lifetime; and (2) Minimizing the total transmission power assigned to all nodes. Maximum lifetime broadcast/multicast routing algorithms [24, 28, 29, 30] can distribute packet- relaying loads for each node in a manner that prevents nodes from being overused or abused. By maximizing the lifetime of all nodes, the time before the network is partitioned is prolonged. A lot of work for the broadcast /multicast [17, 18, 20, 21, 22] using the minimum total transmission power as optimization metric is based on the obvious intuition that conserving power will ensure the network lifetime to be increased. Most recent work has been proposed for the problems of minimizing the energy consumption for broadcasting and multicasting in wireless ad hoc networks, addressed as the MEB (Minimum-Energy Broadcast) problem and MEM (Minimum-Energy Multicast) problem respectively. Since both the MEB problem and the MEM problem, a special case of MEM, have recently been shown to be NP-hard [23, 25], efficient heuristic algorithm design Proceedings of the 12th IEEE International Conference on Network Protocols (ICNP’04) 1092-1648/04 $ 20.00 IEEE