Graph layout problems parameterized by vertex cover

In the framework of parameterized complexity, one of the most commonly used structural parameters is the treewidth of the input graph. The reason for this is that most natural graph problems turn out to be fixed parameter tractable when parameterized by treewidth. However, Graph Layout problems are a notable exception. In particular, no fixed parameter tractable algorithms are known for the Cutwidth, Bandwidth, Imbalance and Distortion problems parameterized by treewidth. In fact, Bandwidth remains NP-complete even restricted to trees. A possible way to attack graph layout problems is to consider structural parameterizations that are stronger than treewidth. In this paper we study graph layout problems parameterized by the size of the minimum vertex cover of the input graph. We show that all the mentioned problems are fixed parameter tractable. Our basic ingredient is a classical algorithm for Integer Linear Programming when parameterized by dimension, designed by Lenstra and later improved by Kannan. We hope that our results will serve to re-emphasize the importance and utility of this algorithm

Age Distribution of Multiple Functionally Relevant Subsets of CD4+ T Cells in Human Blood Using a Standardized and Validated 14-Color EuroFlow Immune Monitoring Tube.

CD4+ T cells comprise multiple functionally distinct cell populations that play a key role in immunity. Despite blood monitoring of CD4+ T-cell subsets is of potential clinical utility, no standardized and validated approaches have been proposed so far. The aim of this study was to design and validate a single 14-color antibody combination for sensitive and reproducible flow cytometry monitoring of CD4+ T-cell populations in human blood to establish normal age-related reference values and evaluate the presence of potentially altered profiles in three distinct disease models-monoclonal B-cell lymphocytosis (MBL), systemic mastocytosis (SM), and common variable immunodeficiency (CVID). Overall, 145 blood samples from healthy donors were used to design and validate a 14-color antibody combination based on extensive reagent testing in multiple cycles of design-testing-evaluation-redesign, combined with in vitro functional studies, gene expression profiling, and multicentric evaluation of manual vs. automated gating. Fifteen cord blood and 98 blood samples from healthy donors (aged 0-89 years) were used to establish reference values, and another 25 blood samples were evaluated for detecting potentially altered CD4 T-cell subset profiles in MBL (n = 8), SM (n = 7), and CVID (n = 10). The 14-color tube can identify ≥89 different CD4+ T-cell populations in blood, as validated with high multicenter reproducibility, particularly when software-guided automated (vs. manual expert-based) gating was used. Furthermore, age-related reference values were established, which reflect different kinetics for distinct subsets: progressive increase of naïve T cells, T-helper (Th)1, Th17, follicular helper T (TFH) cells, and regulatory T cells (Tregs) from birth until 2 years, followed by a decrease of naïve T cells, Th2, and Tregs in older children and a subsequent increase in multiple Th-cell subsets toward late adulthood. Altered and unique CD4+ T-cell subset profiles were detected in two of the three disease models evaluated (SM and CVID). In summary, the EuroFlow immune monitoring TCD4 tube allows fast, automated, and reproducible identification of ≥89 subsets of CD4+ blood T cells, with different kinetics throughout life. These results set the basis for in-depth T-cell monitoring in different disease and therapeutic conditions