Leafy spanning arborescences in DAGs.

Broadcasting in a computer network is a method of transferring a message to all recipients simultaneously. It is common in this situation to use a tree with many leaves to perform the broadcast, as internal nodes have to forward the messages received, while leaves are only receptors. We consider the subjacent problem of, given a directed graph D , finding a spanning arborescence of D , if one exists, with the maximum number of leaves. In this paper, we concentrate on the class of rooted directed acyclic graphs, for which the problem is known to be MaxSNP-hard. A 2-approximation was previously known for this problem on this class of directed graphs. We improve on this result, presenting a 3 2 -approximation. We also adapt a result for the undirected case and derive an inapproximability result for the vertex-weighted version of Maximum Leaf Spanning Arborescence on rooted directed acyclic graphs. [ABSTRACT FROM AUTHOR]