Fixed Parameter Algorithms for DOMINATING SET and Related Problems on Planar Graphs
- J. Alber, H. Bodlaender, H. Fernau, T. Kloks, R. Niedermeier
- MathematicsAlgorithmica
- 1 August 2002
An algorithm is presented that constructively produces a solution to the k -DOMINATING SET problem for planar graphs in time O(c^ \sqrt k n) where c=4^ 6\sqrt 34 and k is the size of the face cover set.
Parametric Duality and Kernelization: Lower Bounds and Upper Bounds on Kernel Size
- Jianer Chen, H. Fernau, Iyad A. Kanj, Ge Xia
- Mathematics, Computer ScienceSIAM journal on computing (Print)
- 24 February 2005
An upper bound of 67k is derived on the problem kernel for planar dominating set improving the previous 335k upper bound by Alber et al.
edge dominating set: Efficient Enumeration-Based Exact Algorithms
- H. Fernau
- Computer Science, MathematicsIWPEC
- 13 September 2006
It is proved that this problem is in FPT for general (weighted) graphs and how the use of compact representations may speed up the decision algorithm is shown.
Parameterized complexity: exponential speed-up for planar graph problems
- J. Alber, H. Fernau, R. Niedermeier
- Mathematics, Computer ScienceJ. Algorithms
- 8 July 2001
On Parameterized Enumeration
- H. Fernau
- Mathematics, Computer ScienceInternational Computing and Combinatorics…
- 15 August 2002
A fixed parameter algorithm is given for the reconfiguration of faulty chips when providing so-called shared and linked spares as well as other enumeration techniques.
Kernel(s) for problems with no kernel: On out-trees with many leaves
- H. Fernau, F. Fomin, D. Lokshtanov, D. Raible, Saket Saurabh, Yngve Villanger
- MathematicsTALG
- 27 October 2008
This work gives 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, and is the first ones separating Karp kernelization from Turing kernelization.
Refined Search Tree Technique for DOMINATING SET on Planar Graphs
- J. Alber, Hongbing Fan, U. Stege
- Mathematics, Computer ScienceInternational Symposium on Mathematical…
- 27 August 2001
A fixed parameter algorithm with running time O(8kn), where k is the size of the dominating set and n is the number of vertices in the graph is derived.
An exact algorithm for the Maximum Leaf Spanning Tree problem
- H. Fernau, Joachim Kneis, P. Rossmanith
- Computer ScienceTheoretical Computer Science
- 2 December 2009
Given an undirected graph G with n nodes, the Maximum Leaf Spanning Tree problem asks to find a spanning tree of G with as many leaves as possible. When parameterized in the number of leaves k, this…
An Efficient Exact Algorithm for Constraint Bipartite Vertex Cover
- H. Fernau, R. Niedermeier
- Computer Science, MathematicsJ. Algorithms
- 6 September 1999
This work provides the first nontrivial so-called "fixed parameter" algorithm for CBVC, running in time O(1.3999k1+k2 + (k1-k2n), which is efficient for small values of k1 and k2, as occurring in applications.
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