Fast branching algorithm for Cluster Vertex Deletion

In the family of clustering problems, we are given a set of objects (vertices of the graph), together with some observed pairwise similarities (edges). The goal is to identify clusters of similar objects by slightly modifying the graph to obtain a cluster graph (disjoint union of cliques). Hueffner et al. [Theory Comput. Syst. 2010] initiated the parameterized study of Cluster Vertex Deletion, where the allowed modification is vertex deletion, and presented an elegant O(2^k * k^9 + n * m)-time fixed-parameter algorithm, parameterized by the solution size. In our work, we pick up this line of research and present an O(1.9102^k * (n + m))-time branching algorithm

Bounded Search Tree Algorithms for Parameterized Cograph Deletion: Efficient Branching Rules by Exploiting Structures of Special Graph Classes

Many fixed-parameter tractable algorithms using a bounded search tree have been repeatedly improved, often by describing a larger number of branching rules involving an increasingly complex case analysis. We introduce a novel and general search strategy that branches on the forbidden subgraphs of a graph class relaxation. By using the class of $P_4$-sparse graphs as the relaxed graph class, we obtain efficient bounded search tree algorithms for several parameterized deletion problems. We give the first non-trivial bounded search tree algorithms for the cograph edge-deletion problem and the trivially perfect edge-deletion problems. For the cograph vertex deletion problem, a refined analysis of the runtime of our simple bounded search algorithm gives a faster exponential factor than those algorithms designed with the help of complicated case distinctions and non-trivial running time analysis [21] and computer-aided branching rules [11].Comment: 23 pages. Accepted in Discrete Mathematics, Algorithms and Applications (DMAA

Polynomial kernels for 3-leaf power graph modification problems

A graph G=(V,E) is a 3-leaf power iff there exists a tree T whose leaves are V and such that (u,v) is an edge iff u and v are at distance at most 3 in T. The 3-leaf power graph edge modification problems, i.e. edition (also known as the closest 3-leaf power), completion and edge-deletion, are FTP when parameterized by the size of the edge set modification. However polynomial kernel was known for none of these three problems. For each of them, we provide cubic kernels that can be computed in linear time for each of these problems. We thereby answer an open problem first mentioned by Dom, Guo, Huffner and Niedermeier (2005).Comment: Submitte

Metal-Substituted Microporous Aluminophosphates

This chapter aims to present the zeotypes aluminophosphates (AlPOs) as a complementary alternative to zeolites in the isomorphic incorporation of metal ions within all-inorganic microporous frameworks as well as to discuss didactically the catalytic consequences derived from the distinctive features of both frameworks. It does not intend to be a compilation of either all or the most significant publications involving metal-substituted microporous aluminophosphates. Families of AlPOs and zeolites, which include metal ion-substituted variants, are the dominant microporous materials. Both these systems are widely used as catalysts, in particular through aliovalent metal ions substitution. Here, some general description of the synthesis procedures and characterization techniques of the MeAPOs (metal-contained aluminophosphates) is given along with catalytic properties. Next, some illustrative examples of the catalytic possibilities of MeAPOs as catalysts in the transformation of the organic molecules are given. The oxidation of the hardly activated hydrocarbons has probably been the most successful use of AlPOs doped with the divalent transition metal ions Co2+, Mn2+, and Fe2+, whose incorporation in zeolites is disfavoured. The catalytic role of these MeAPOs is rationalized based on the knowledge acquired from a combination of the most advanced characterization techniques. Finally, the importance of the high specificity of the structure-directing agents employed in the preparation of MeAPOs is discussed taking N,N-methyldicyclohexylamine in the synthesis of AFI-structured materials as a driving force. It is shown how such a high specificity could be predicted and how it can open great possibilities in the control of parameters as critical in catalysis as crystal size, inter-and intracrystalline mesoporosity, acidity, redox properties, incorporation of a great variety of heteroatom ions or final environment of the metal site (surrounding it by either P or Al)