Relay Placement in Wireless Networks: Minimizing Communication Cost

Given n source nodes and k relay nodes, we model the optimal relay topology problem allowing for simultaneous optimization of the relay node locations and traffic through the network, so that the overall number of packet retransmissions is minimized. We argue that state-of-the-art models and algorithms for relay placement in wireless networks do not reflect salient characteristics of the optimal relays topology and lead to suboptimal solutions. We do not constrain the position of relays to a finite set of discrete points, as the latter may not be feasible in practical networks. In this case, we show that just listing a set of feasible sites for the relays is already at least APX-hard. Exploiting convexity in a special case of the network communication cost function, we give an optimal algorithm for the relay placement problem. However, the algorithm is exponential on the number of nodes in the network. We suggest a practical heuristic algorithm for relay placement: RePlace. We compare RePlace numerically to the optimal algorithm and show that RePlace achieves the optimal or almost optimal solutions. We implement RePlace in the full network stack simulator JiST/SWANS. The relay topologies generated by RePlace eliminate overhead communication cost almost entirely.