Min-cost wireless multihop networks in Euclidean space

Space information flow is a new problem recently proposed by Li and Wu [1]. It studies the transmission of information in a geometric space, where information flows are free to propagate along any trajectories, and may be encoded wherever they meet. This work studies the wireless version of the space information flow problem, which models the planning of a wireless multihop network with fixed terminals in an Euclidean space. Additional relay nodes can be inserted at any location. The goal is to minimize the total cost of the wireless multihop network, while sustaining end-to-end unicast/multicast communication demands among terminals at known coordinates. We first formulate such cost minimization into a mathematical optimization problem, and examine its convexity. A generic solution that encompasses a resource allocation scheme, a flow routing scheme and a relay localization scheme is designed. A series of methods that can substantially reduce the complexity of solving the optimization problem are discussed. Finally, the algorithms are illustrated and verified by simulation studies.