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In the Cluster Editing problem, a graph is to be changed to a disjoint union of cliques by at most k operations of edge insertion or edge deletion. Improving on the best previously known quadratic-size polynomial-time kernelization, we describe how a crown-type structural reduction rule can be used to obtain a 6k kernelization bound.
In this paper, we study the cluster editing problem which is fixed parameter tractable. We present the first practical implementation of a FPT based method for cluster editing, using the approach in [6,7], and compare our implementation with the straightforward greedy method and a solution based on linear programming [3]. Our experiments show that the best(More)
Many types of plant cell retain their developmental plasticity and have the capacity to switch fate when exposed to a new source of positional information. In the root epidermis of Arabidopsis, cells differentiate in alternating files of hair cells and non-hair cells, in response to positional information and the activity of the homoeodomain transcription(More)
We introduce a family of algebras which are multiplicative analogues of preprojective algebras, and their deformations, as introduced by M. P. Holland and the first author. We show that these algebras provide a natural setting for the 'middle convolution' operation introduced by N. M. Katz in his book 'Rigid local systems', and put in an algebraic setting(More)
It has long intrigued researchers why some but not all organisms can regenerate missing body parts. Plants are remarkable in that they can regenerate the entire organism from a small piece of tissue, or even a single cell. Epigenetic mechanisms that control chromatin organization are now known to regulate the cellular plasticity and reprogramming necessary(More)
Eukaryotic chromosomes occupy distinct territories within interphase nuclei. The arrangement of chromosome territories (CTs) is important for replication, transcription, repair and recombination processes. Our knowledge about interphase chromatin arrangement is mainly based on results from in situ labeling approaches. The phylogenetic affiliation of a(More)
A new Arabidopsis meiotic mutant has been isolated. Homozygous ahp2-1 (Arabidopsis homologue pairing 2) plants were sterile because of failure of both male and female gametophyte development. Fluorescent in situ hybridisation showed that in ahp2-1 male meiocytes, chromosomes did not form bivalents during prophase I and instead seemed to associate(More)
The two objectives of this paper are: (1) to articulate three new general techniques for designing FPT algorithms, and (2) to apply these to obtain new FPT algorithms for Set Splitting and Vertex Cover. In the case of Set Splitting, we improve the best previous O * (72 k) FPT algorithm due to Dehne, Fellows and Rosamond [DFR03], to O * (8 k) by an approach(More)
The problem of packing k edge-disjoint triangles in a graph has been thoroughly studied both in the classical complexity and the approximation fields and it has a wide range of applications in many areas, especially computational biology [BP96]. In this paper we present an analysis of the problem from a parameterized complexity viewpoint. We describe a(More)