  Trees with many leaves have applications on broadcasting, which is a method
in networks for transferring a message to all recipients simultaneously.
Internal nodes of a broadcasting tree require more expensive technology,
because they have to forward the messages received. We address a problem that
captures the main goal, which is to find spanning trees with few internal nodes
in a given network. The Maximum Leaf Spanning Arborescence problem consists of,
given a directed graph D, finding a spanning arborescence of D, if one exists,
with the maximum number of leaves. This problem is known to be NP-hard in
general and MaxSNP-hard on the class of rooted directed acyclic graphs. In this
paper, we explore a relation between Maximum Leaf Spanning Arborescence in
rooted directed acyclic graphs and maximum weight set packing. The latter
problem is related to independent sets on particular classes of intersection
graphs. Exploiting this relation, we derive a 7/5-approximation for Maximum
Leaf Spanning Arborescence on rooted directed acyclic graphs, improving on the
previous 3/2-approximation. The approach used might lead to improvements on the
best approximation ratios for the weighted k-set packing problem.
