Labeling Schemes for Deterministic Radio Multi-Broadcast

We consider the multi-broadcast problem in arbitrary connected radio networks consisting of $n$ nodes. There are $k$ designated source nodes for some fixed $k\in \{1,\dots ,n\}$, and each source node has a distinct piece of information that it wants to share with all nodes in the network. We set out to determine the shortest possible labels so that multi-broadcast can be solved deterministically in the labeled radio network by some universal deterministic distributed algorithm.