25 research outputs found

    NLC-2 graph recognition and isomorphism

    Get PDF
    NLC-width is a variant of clique-width with many application in graph algorithmic. This paper is devoted to graphs of NLC-width two. After giving new structural properties of the class, we propose a O(n2m)O(n^2 m)-time algorithm, improving Johansson's algorithm \cite{Johansson00}. Moreover, our alogrithm is simple to understand. The above properties and algorithm allow us to propose a robust O(n2m)O(n^2 m)-time isomorphism algorithm for NLC-2 graphs. As far as we know, it is the first polynomial-time algorithm.Comment: soumis \`{a} WG 2007; 12

    Extending Partial Representations of Circle Graphs

    No full text
    The partial representation extension problem is a recently introduced generalization of the recognition problem. A circle graph is an intersection graph of chords of a circle. We study the partial representation extension problem for circle graphs, where the input consists of a graph G and a partial representation R′ giving some pre-drawn chords that represent an induced subgraph of G. The question is whether one can extend R′ to a representation R of the entire G, i.e., whether one can draw the remaining chords into a partially pre-drawn representation. Our main result is a polynomial-time algorithm for partial representation extension of circle graphs. To show this, we describe the structure of all representation a circle graph based on split decomposition. This can be of an independent interest

    Prediction of Immunotherapy Response in Melanoma through Combined Modeling of Neoantigen Burden and Immune-Related Resistance Mechanisms

    No full text
    Abstract Purpose: While immune checkpoint blockade (ICB) has become a pillar of cancer treatment, biomarkers that consistently predict patient response remain elusive due to the complex mechanisms driving immune response to tumors. We hypothesized that a multi-dimensional approach modeling both tumor and immune-related molecular mechanisms would better predict ICB response than simpler mutation-focused biomarkers, such as tumor mutational burden (TMB). Experimental Design: Tumors from a cohort of patients with late-stage melanoma (n = 51) were profiled using an immune-enhanced exome and transcriptome platform. We demonstrate increasing predictive power with deeper modeling of neoantigens and immune-related resistance mechanisms to ICB. Results: Our neoantigen burden score, which integrates both exome and transcriptome features, more significantly stratified responders and nonresponders (P = 0.016) than TMB alone (P = 0.049). Extension of this model to include immune-related resistance mechanisms affecting the antigen presentation machinery, such as HLA allele-specific LOH, resulted in a composite neoantigen presentation score (NEOPS) that demonstrated further increased association with therapy response (P = 0.002). Conclusions: NEOPS proved the statistically strongest biomarker compared with all single-gene biomarkers, expression signatures, and TMB biomarkers evaluated in this cohort. Subsequent confirmation of these findings in an independent cohort of patients (n = 110) suggests that NEOPS is a robust, novel biomarker of ICB response in melanoma. </jats:sec
    corecore