Spanning trees with many leaves
SIAM Journal on Discrete Mathematics
Spanning trees in graphs of minimum degree 4 or 5
Discrete Mathematics
A short note on the approximability of the maximum leaves spanning tree problem
Information Processing Letters
Approximating maximum leaf spanning trees in almost linear time
Journal of Algorithms
Vertex cover: further observations and further improvements
Journal of Algorithms
FST TCS 2000 Proceedings of the 20th Conference on Foundations of Software Technology and Theoretical Computer Science
2-Approximation Algorithm for Finding a Spanning Tree with Maximum Number of Leaves
ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Invitation to data reduction and problem kernelization
ACM SIGACT News
Parametric Duality and Kernelization: Lower Bounds and Upper Bounds on Kernel Size
SIAM Journal on Computing
Spanning trees with many leaves
Journal of Graph Theory
Solving Connected Dominating Set Faster than 2 n
Algorithmica - Parameterized and Exact Algorithms
Tight Bounds and a Fast FPT Algorithm for Directed Max-Leaf Spanning Tree
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
A New Algorithm for Finding Trees with Many Leaves
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
On problems without polynomial kernels
Journal of Computer and System Sciences
Spanning Directed Trees with Many Leaves
SIAM Journal on Discrete Mathematics
FPT algorithms and kernels for the Directedk- Leaf problem
Journal of Computer and System Sciences
Kernelization: New Upper and Lower Bound Techniques
Parameterized and Exact Computation
On Finding Directed Trees with Many Leaves
Parameterized and Exact Computation
A 4k2 kernel for feedback vertex set
ACM Transactions on Algorithms (TALG)
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
An approximation algorithm for the maximum leaf spanning arborescence problem
ACM Transactions on Algorithms (TALG)
Satisfiability allows no nontrivial sparsification unless the polynomial-time hierarchy collapses
Proceedings of the forty-second ACM symposium on Theory of computing
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
The lost continent of polynomial time: preprocessing and kernelization
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
A faster exact algorithm for the directed maximum leaf spanning tree problem
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
An exact exponential-time algorithm for the Directed Maximum Leaf Spanning Tree problem
Journal of Discrete Algorithms
Parameterized algorithms for directed maximum leaf problems
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Parameterized Complexity
Preprocessing subgraph and minor problems: When does a small vertex cover help?
Journal of Computer and System Sciences
A 9k kernel for nonseparating independent set in planar graphs
Theoretical Computer Science
Beyond bidimensionality: Parameterized subexponential algorithms on directed graphs
Information and Computation
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The k-Leaf Out-Branching problem is to find an out-branching, that is a rooted oriented spanning tree, with at least k leaves in a given digraph. The problem has recently received much attention from the viewpoint of parameterized algorithms. Here, we take a kernelization based approach to the k-Leaf-Out-Branching problem. We give the first polynomial kernel for Rooted k-Leaf-Out-Branching, a variant of k-Leaf-Out-Branching where the root of the tree searched for is also a part of the input. Our kernel with O(k3) vertices is obtained using extremal combinatorics. For the k-Leaf-Out-Branching problem, we show that no polynomial-sized kernel is possible unless coNP is in NP/poly. However, our positive results for Rooted k-Leaf-Out-Branching immediately imply that the seemingly intractable k-Leaf-Out-Branching problem admits a data reduction to n independent polynomial-sized kernels. These two results, tractability and intractability side by side, are the first ones separating Karp kernelization from Turing kernelization. This answers affirmatively an open problem regarding “cheat kernelization” raised by Mike Fellows and Jiong Guo independently.