Reduction Techniques for Graph Isomorphism in the Context of Width Parameters

We study the parameterized complexity of the graph isomorphism problem when parameterized by width parameters related to tree decompositions. We apply the following technique to obtain fixed-parameter tractability for such parameters. We first compute an isomorphism invariant set of potential bags for a decomposition and then apply a restricted version of the Weisfeiler-Lehman algorithm to solve isomorphism. With this we show fixed-parameter tractability for several parameters and provide a unified explanation for various isomorphism results concerned with parameters related to tree decompositions. As a possibly first step towards intractability results for parameterized graph isomorphism we develop an fpt Turing-reduction from strong tree width to the a priori unrelated parameter maximum degree.Comment: 23 pages, 4 figure

Computing: report leaps geographical barriers but stumbles over gender

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/62917/1/441025a.pd

Confirmation of association of the GABRA2 gene with alcohol dependence by subtype-specific analysis

Objectives: Three recent studies revealed a haplotypic association of alcohol dependence with the gene encoding the {alpha}2 subunit of the {gamma}-aminobutyric acid type A (GABAA) receptor (GABRA2). The present study examined whether variation of the GABRA2 gene confers susceptibility to different subtypes of alcohol dependence in the German population. Methods: A total of 257 German alcohol-dependent patients and 88 healthy population controls were genotyped for six single-nucleotide polymorphisms covering the middle part and the 3′ end of GABRA2. Allelic, genotypic and haplotypic comparisons were done for subgroups of alcohol-dependent patients with a presumed high genetic load. Results: The overall alcohol-dependent patients vs. control group comparison confirmed positive allelic association for five of six single-nucleotide polymorphisms mapping from intron 3 to the 3′ end of GABRA2 (P=0.01–0.02). Haplotype analysis revealed two common haplotypes accounting for approximately 90% of the chromosomes within the patients and controls. The less frequent haplotype was significantly more prevalent among the alcohol-dependent patients (45%) than among the controls [29%; odds ratio (OR)=1.97, 95% confidence interval (CI): 1.30–2.96]. The strength of association increased, if the subsets of alcohol-dependent patients with a positive family history (OR=2.60, 95% CI: 1.63–4.13), withdrawal seizures (OR=2.22, 95% CI: 1.30–3.79) or an early onset (OR=2.19, 95% CI: 1.24–3.88) were analyzed. Conclusions: Although our study was limited by the number of cases being larger than the number of controls, the results confirm GABRA2 as a susceptibility gene for alcohol dependence in the German population. We found a consistent increase of the susceptibility effect in alcohol-dependent patients with a presumed strong genetic predisposition