In wireless sensor networks, energy efficiency is generally achieved by turning off some capabilities from a subset of deployed sensors. The set of active nodes must therefore meet the application requirements (e.g. area coverage and data redundancy) while remaining fully connected to allow further data collection. Here, the authors focus on the case of a nomad sink entering the network and gathering every monitoring data. At the routing layer, minimizing the number of nodes acting as relays requires to construct a Maximum Leaf Spanning Tree (MLST). However, optimizing converge cast communications consists in minimizing the hop distance between the sink and all others nodes, leading so to a shortest path tree rooted at the sink.