PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Parameterized Algorithms for Directed Maximum Leaf Problems
N Alon, F Fomin, Gregory Gutin, M Krivelevich and S Saurabh
In: ICALP 2007, 9–13 July 2007, Wrocław, Poland.


We prove that finding a rooted subtree with at least $k$ leaves in a directed graph is a fixed parameter tractable problem. A similar result holds for finding rooted spanning trees with many leaves in strongly connected directed graphs. This settles completely an open question of Fellows and solves another one for strongly connected directed graphs. 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: Every strongly connected digraph on $n$ vertices with minimum in-degree at least $3$, contains a rooted spanning tree with at least $(n/2)^{1/5}$ leaves.

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EPrint Type:Conference or Workshop Item (Paper)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:3489
Deposited By:Gregory Gutin
Deposited On:11 February 2008