Leafy Spanning Arborescences in DAGs

How heavy independent sets help to find arborescences with many leaves in DAGs

“…Then we will deduce that the modified version of Maxleaves-W3DM that uses SquareImp, instead of an approximation for maximum weight 3D-matching, achieves a ratio of 3/2 for Maximum Leaf Spanning Arborescence on rooted dags. This ratio matches the best known for rooted dags, given by another algorithm presented in [10].…”

“…We have described in [10] an algorithm for Maximum Leaf Spanning Arborescence on rooted dags called Maxleaves-W3DM. It uses as a black box an approximation for maximum weight 3D-matching (hence the W3DM acronym).…”

“…The idea we will explore is to build directly an instance of wMIS and to apply an approximation for wMIS on this instance. An adapted version of a result from [10] allows us to deduce that the modified version of Maxleaves-W3DM that uses an approximation for wMIS instead of an approximation for maximum weight 3D-matching preserves the ratio from the approximation for wMIS, up to 4/3.…”

“…The instances of wMIS in the translated construction use only weights 1 and 2, hence we call the resulting algorithm Maxleaves-12MIS. To describe the algorithm in details, we reproduce some definitions and figures from [10].…”

“…Section 5 concludes that the new algorithm is a 3/2-approximation for Maximum Leaf Spanning Arborescence on rooted dags. In Section 6, we present our main result: a 7/5-approximation for Maximum Leaf Spanning Arborescence on rooted dags that uses ingredients from the 3/2-approximation in [10] to tune the 3/2-approximation from Section 3. The new approximation relies on a new 7/5-approximation on the subclass of weighted 4-claw free graphs considered in Section 4.…”