Parameterized algorithms for directed maximum leaf problems

Noga Alon, Fedor V. Fomin, Gregory Gutin, Michael Krivelevich, Saket Saurabh

Research output: Chapter in Book/Report/Conference proceedingConference contribution

17 Scopus citations


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.

Original languageEnglish (US)
Title of host publicationAutomata, Languages and Programming - 34th International Colloquium, ICALP 2007, Proceedings
PublisherSpringer Verlag
Number of pages11
ISBN (Print)3540734198, 9783540734192
StatePublished - 2007
Externally publishedYes
Event34th International Colloquium on Automata, Languages and Programming, ICALP 2007 - Wroclaw, Poland
Duration: Jul 9 2007Jul 13 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4596 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other34th International Colloquium on Automata, Languages and Programming, ICALP 2007

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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