An FPT Algorithm for Directed Spanning k-Leaf
| dc.creator | Bonsma, Paul | |
| dc.creator | Dorn, Frederic | |
| dc.date | 2007-11-26 | |
| dc.date.accessioned | 2026-07-07T08:45:00Z | |
| dc.date.available | 2026-07-07T08:45:00Z | |
| dc.description | 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 directed graph 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(k^3) can be found. This enables a dynamic programming based algorithm of running time 2^{O(k^3 \log k)} n^{O(1)}, where n=|V(D)|. | |
| dc.description | 17 pages, 8 figures | |
| dc.identifier | https://arxiv.org/abs/0711.4052 | |
| dc.identifier | http://arxiv.org/abs/0711.4052 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142854 | |
| dc.subject | Data Structures and Algorithms | |
| dc.subject | Discrete Mathematics | |
| dc.title | An FPT Algorithm for Directed Spanning k-Leaf | |
| dc.type | text |