TY - GEN
T1 - Parameterized algorithms for directed maximum leaf problems
AU - Alon, Noga
AU - Fomin, Fedor V.
AU - Gutin, Gregory
AU - Krivelevich, Michael
AU - Saurabh, Saket
PY - 2007/1/1
Y1 - 2007/1/1
N2 - We prove that finding a rooted subtree with at least k leaves in a digraph is a fixed parameter tractable problem. A similar result holds for finding rooted spanning trees with many leaves in digraphs from a wide family ℒ that includes all strong and acyclic digraphs. This settles completely an open question of Fellows and solves another one for digraphs in ℒ. Our algorithms are based on the following combinatorial result which can be viewed as a generalization of many results for a 'spanning tree with many leaves' in the undirected case, and which is interesting on its own: If a digraph D ∈ ℒ of order n with minimum in-degree at least 3 contains a rooted spanning tree, then D contains one with at least (n/2)1/5 - 1 leaves.
AB - We prove that finding a rooted subtree with at least k leaves in a digraph is a fixed parameter tractable problem. A similar result holds for finding rooted spanning trees with many leaves in digraphs from a wide family ℒ that includes all strong and acyclic digraphs. This settles completely an open question of Fellows and solves another one for digraphs in ℒ. Our algorithms are based on the following combinatorial result which can be viewed as a generalization of many results for a 'spanning tree with many leaves' in the undirected case, and which is interesting on its own: If a digraph D ∈ ℒ of order n with minimum in-degree at least 3 contains a rooted spanning tree, then D contains one with at least (n/2)1/5 - 1 leaves.
UR - https://www.scopus.com/pages/publications/38149141655
U2 - 10.1007/978-3-540-73420-8_32
DO - 10.1007/978-3-540-73420-8_32
M3 - Conference contribution
AN - SCOPUS:38149141655
SN - 3540734198
SN - 9783540734192
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 352
EP - 362
BT - Automata, Languages and Programming - 34th International Colloquium, ICALP 2007, Proceedings
PB - Springer Verlag
T2 - 34th International Colloquium on Automata, Languages and Programming, ICALP 2007
Y2 - 9 July 2007 through 13 July 2007
ER -