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FSTTCS
2007
Springer

Better Algorithms and Bounds for Directed Maximum Leaf Problems

8 years 9 months ago
Better Algorithms and Bounds for Directed Maximum Leaf Problems
The Directed Maximum Leaf Out-Branching problem is to find an out-branching (i.e. a rooted oriented spanning tree) in a given digraph with the maximum number of leaves. In this paper, we improve known parameterized algorithms and combinatorial bounds on the number of leaves in out-branchings. We show that – every strongly connected digraph D of order n with minimum indegree at least 3 has an out-branching with at least (n/4)1/3 − 1 leaves; – if a strongly connected digraph D does not contain an out-branching with k leaves, then the pathwidth of its underlying graph is O(k log k); – it can be decided in time 2O(k log2 k) · nO(1) whether a strongly connected digraph on n vertices has an out-branching with at least k leaves. All improvements use properties of extremal structures obtained after applying local search and properties of some out-branching decompositions.
Noga Alon, Fedor V. Fomin, Gregory Gutin, Michael
Added 07 Jun 2010
Updated 07 Jun 2010
Type Conference
Year 2007
Where FSTTCS
Authors Noga Alon, Fedor V. Fomin, Gregory Gutin, Michael Krivelevich, Saket Saurabh
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