Abstract not found

) B. Courcelle 1;? and J.A. Makowsky 2;3;?? 1 LaBRI Universite Bordeaux-1, Talence, France e{mail: courcell@labri.u-bordeaux.fr 2 Department of Computer Science Technion{Israel Institute of Technology, Haifa, Israel e{mail: janos@cs.technion.ac.il 3 Department of Mathematics Swiss Federal Institute of Technology 8092 Zurich, Switzerland Abstract. Tree-like structures are usually dened by construction from small structures or, equivalently, by "decompositions" as in treedecompositions or modular decompositions, or alternatively by transductions from trees. All of these approaches lead to parametrized classes of structures for which many classical problems become parametrically tractable. We study the interrelationships between these approaches. The main novelty of this paper is to enrich the set of operations dening clique-width with a new operation that fuses in one stroke all vertices having a designated label. Adding this fuse operation to the operations ...

We study the parametrized complexity of the knot (and link) polynomials known as Jones polynomials, Kauffman polynomials and Homfly-polynomials. It is known that computing these polynomials is ]P hard in general. We look for parameters of the combinatorial presentation of knots and links which make the computation of these polynomials to be fixed parameter tractable, i.e. to be in FPT . If the link is explicitly presented as a closed braid, the number of its strands is known to be such a parameter. In a generalization thereof, if the link is explicitly presented as a combination of compositions and rotations of k-tangles the link is called k-algebraic, and its algebraicity k is such a parameter. The previously known proofs that for this parameter the link polynomials are in FPT uses the so called skein-modules, and is algebraic in its nature.