Inhalt des Dokuments
Preprint 46-2007
Combinatorial Optimization & Graph Algorithms group (COGA-Preprints)- Title
- An FPT Algorithm for Directed Spanning k-Leaf
- Authors
- Paul Bonsma and Frederic Dorn
- Classification
-
not available
- Keywords
-
FPT algorithm, maximum leaf, directed graph, spanning tree, out-branching
- Abstract
-
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(k^3 log k) nO(1), where n=|V(D)|.
- Source
- Download as [PDF]
Zusatzinformationen / Extras
Direktzugang
Schnellnavigation zur Seite über Nummerneingabe