A New Algorithm for Finding Trees with Many Leaves

We present an algorithm that finds out-trees and out-branchings with at least k leaves in directed graphs. These problems are known as Directed Maximum Leaf Out-Tree and Directed Maximum Leaf Out-Branching, respectively, and—in the case of undirected graphs—as Maximum Leaf Spanning Tree. The run time of our algorithm is O(4 ^k nm) on directed graphs and O(poly(n)+4 ^k k ²) on undirected graphs. This improves over the previously fastest algorithms for these problems with run times of 2 ^O(klog k) poly(n) and O(poly(n)+6.75 ^k poly(k)) respectively.