Parallel implementations of combinations of broadcast, reduction and scan

Broadcast, reduction and scan are popular functional skeletons which are used in distributed algorithms to distribute and gather data. The authors derive new parallel implementations of combinations of broadcast, reduction and scan via a tabular classification of linearly recursive functions. The trick in the derivation is to not simply combine the individual parallel implementations of broadcast, reduction and scan, but to transform these combinations to skeletons with a better performance. These skeletons are also linearly recursive.