Repository: DepositOnce – institutional repository for research data and publications of TU Berlin https://depositonce.tu-berlin.de
TY - RPRT
AU - Bonsma, Paul
AU - Dorn, Frederic
PY - 2007
TI - An FPT Algorithm for Directed Spanning k-Leaf
DO - 10.14279/depositonce-14380
UR - http://dx.doi.org/10.14279/depositonce-14380
PB - Technische Universität Berlin
LA - en
AB - An out-branching of a directed graph is a rooted spanning tree with all arcs directed outwards from the root. We consider the problem of deciding whether a given digraph D has an out-branching with at least k leaves (Directed Spanning k-Leaf). We prove that this problem is fixed parameter tractable, when k is chosen as the parameter. Previously this was only known for restricted classes of directed graphs. The main new ingredient in our approach is a lemma that shows that given a locally optimal out-branching of a directed graph in which every arc is part of at least one out-branching, either an out-branching with at least k leaves exists, or a path decomposition with width O(k3) can be found. This enables a dynamic programming based algorithm of running time 2O(k3logk)·nO(1), where n=|V(D)|
KW - FPT algorithm
KW - maximum leaf
KW - directed graph
KW - spanning tree
KW - out-branching
ER -