A Fast Mixed Integer Programming Formulation for Minimum-Power Broadcasting in Wireless Networks

Broadcasting means the distribution of packets from a certain source to all other hosts. One of the possible efficient implementations of broadcasting is to construct a spanning tree rooted at a given source such that each host can receive a copy of the broadcast packet originating from the source. Since the operations of most hosts in wireless networks mainly rely on battery power, in this paper we will focus on the issue of establishing a minimum-power broadcast tree in wireless networks, which has been proven to be NP-complete. Based on the concepts of integer programming and network flow, several mixed integer programming formulations with the capability of constructing a minimum-power broadcast tree have been proposed. In this paper, we will design a set of valid inequalities to speed up the findings of minimum-power broadcast trees. Computer simulations point out that compared with existing formulations, our new inequalities can reduce execution time significantly

Optimization Methods for Minimum Power Multicasting in Wireless Networks with Sectored Antennas

Abstract — We consider the problem of minimum power multicasting in wireless networks with sectored antennas. For omnidirectional wireless broadcast to a node, a transmission from node i to node j will also reach all nodes which are closer to i than j. Depending on the network geometry, this strategy can be highly power efficient. In ideal sectored antenna systems, however, this phenomenon is sector specific; i.e., only those nodes which are located in the same sector as j will receive the transmission implicitly. Though this might seem an apparent disadvantage, the higher gains associated with directional antennas (as opposed to omni-directional antennas) allow for reduced transmission powers without sacrificing the signal-to-interference ratio at the receiver. In this paper, we first develop a mixed integer linear programming model for optimal solution of the minimum power multicast problem with sectored antennas. Subsequently, we discuss a biologically inspired algorithm for solving the problem to near-optimality at a very reasonable computation time. Experiments on randomly generated 10, 20 and 30-node networks indicate that near-optimal solutions can be obtained using the proposed algorithm. I