scholarly journals New clique and independent set algorithms for circle graphs

1992 ◽  
Vol 36 (1) ◽  
pp. 1-24 ◽  
Author(s):  
Alberto Apostolico ◽  
Mikhail J. Atallah ◽  
Susanne E. Hambrusch
Keyword(s):  
Independent Set ◽  
Circle Graphs

scholarly journals New clique and independent set algorithms for circle graphs

1993 ◽  
Vol 41 (2) ◽  
pp. 179-180 ◽  
Author(s):  
Alberto Apostolico ◽  
Mikhail J. Atallah ◽  
Susanne Hambrusch
Keyword(s):  
Independent Set ◽  
Circle Graphs

Approximation algorithms for maximum weight k-coverings of graphs by packings

2021 ◽  
pp. 2150099
Author(s):  
Fanica Gavril ◽  
Mordechai Shalom ◽  
Shmuel Zaks
Keyword(s):  
Approximation Algorithms ◽  
Independent Set ◽  
Connected Component ◽  
Maximum Weight ◽  
Induced Subgraph ◽  
Circle Graphs ◽  
Vertex Set ◽  
Induced Matchings ◽  
Closed Neighborhood ◽  
Vertex Disjoint

Let [Formula: see text] be a family of graphs and let [Formula: see text] be a set of connected graphs, each with at most [Formula: see text] vertices, [Formula: see text] fixed. A [Formula: see text]-packing of a graph GA is a vertex induced subgraph of GA with every connected component isomorphic to a member of [Formula: see text]. A maximum weight [Formula: see text]-covering of a graph GA by [Formula: see text]-packings, is a maximum weight subgraph of GA exactly covered by [Formula: see text] vertex disjoint [Formula: see text]-packings. For a graph [Formula: see text] let [Formula: see text](GA) be a graph, every vertex [Formula: see text] of which corresponds to a vertex subgraph [Formula: see text] of GA isomorphic to a member of [Formula: see text], two vertices [Formula: see text] of [Formula: see text](GA) being adjacent if and only if [Formula: see text] and [Formula: see text] have common vertices or interconnecting edges. The closed neighborhoods containment graph [Formula: see text] of a graph [Formula: see text], is the graph with vertex set [Formula: see text] and edges directed from vertices [Formula: see text] to [Formula: see text] if and only if they are adjacent in GA and the closed neighborhood of [Formula: see text] is contained in the closed neighborhood of [Formula: see text]. A graph [Formula: see text] is a [Formula: see text] reduced graph if it can be obtained from a graph [Formula: see text] by deleting the edges of a transitive subgraph [Formula: see text] of CNCG(GA). We describe 1.582-approximation algorithms for maximum weight [Formula: see text]-coverings by [Formula: see text]-packings of [Formula: see text] and [Formula: see text] reduced graphs when [Formula: see text] is vertex hereditary, has an algorithm for maximum weight independent set and [Formula: see text]. These algorithms can be applied to families of interval filament, subtree filament, weakly chordal, AT-free and circle graphs, to find 1.582 approximate maximum weight [Formula: see text]-coverings by vertex disjoint induced matchings, dissociation sets, forests whose subtrees have at most [Formula: see text] vertices, etc.

Prediction of K562 Cells Functional Inhibitors Based on Machine Learning Approaches

2020 ◽  
Vol 25 (40) ◽  
pp. 4296-4302 ◽  
Author(s):  
Yuan Zhang ◽  
Zhenyan Han ◽  
Qian Gao ◽  
Xiaoyi Bai ◽  
Chi Zhang ◽  
...  
Keyword(s):  
Machine Learning ◽  
Inclusion Bodies ◽  
Cross Validation ◽  
Independent Set ◽  
K562 Cells ◽  
Machine Learning Algorithms ◽  
Learning Approaches ◽  
Validation Test ◽  
Excess Number ◽  
Fold Cross Validation

Background: β thalassemia is a common monogenic genetic disease that is very harmful to human health. The disease arises is due to the deletion of or defects in β-globin, which reduces synthesis of the β-globin chain, resulting in a relatively excess number of α-chains. The formation of inclusion bodies deposited on the cell membrane causes a decrease in the ability of red blood cells to deform and a group of hereditary haemolytic diseases caused by massive destruction in the spleen. Methods: In this work, machine learning algorithms were employed to build a prediction model for inhibitors against K562 based on 117 inhibitors and 190 non-inhibitors. Results: The overall accuracy (ACC) of a 10-fold cross-validation test and an independent set test using Adaboost were 83.1% and 78.0%, respectively, surpassing Bayes Net, Random Forest, Random Tree, C4.5, SVM, KNN and Bagging. Conclusion: This study indicated that Adaboost could be applied to build a learning model in the prediction of inhibitors against K526 cells.

Predicting Hub Genes of Glioblastomas Based on Support Vector Machine Combined with CFS algorithms

2020 ◽  
Vol 15 ◽  
Author(s):  
Chun Qiu ◽  
Sai Li ◽  
Shenghui Yang ◽  
Lin Wang ◽  
Aihui Zeng ◽  
...  
Keyword(s):  
Support Vector Machine ◽  
Expression Profiles ◽  
Independent Set ◽  
Classification Model ◽  
Support Vector ◽  
Feature Subset ◽  
Hub Genes ◽  
Effective Prevention ◽  
Key Genes ◽  
Control Samples

Aim: To search the genes related to the mechanisms of the occurrence of glioma and to try to build a prediction model for glioblastomas. Background: The morbidity and mortality of glioblastomas are very high, which seriously endangers human health. At present, the goals of many investigations on gliomas are mainly to understand the cause and mechanism of these tumors at the molecular level and to explore clinical diagnosis and treatment methods. However, there is no effective early diagnosis method for this disease, and there are no effective prevention, diagnosis or treatment measures. Methods: First, the gene expression profiles derived from GEO were downloaded. Then, differentially expressed genes (DEGs) in the disease samples and the control samples were identified. After that, GO and KEGG enrichment analyses of DEGs were performed by DAVID. Furthermore, the correlation-based feature subset (CFS) method was applied to the selection of key DEGs. In addition, the classification model between the glioblastoma samples and the controls was built by an Support Vector Machine (SVM) based on selected key genes. Results and Discussion: Thirty-six DEGs, including 17 upregulated and 19 downregulated genes, were selected as the feature genes to build the classification model between the glioma samples and the control samples by the CFS method. The accuracy of the classification model by using a 10-fold cross-validation test and independent set test was 76.25% and 70.3%, respectively. In addition, PPP2R2B and CYBB can also be found in the top 5 hub genes screened by the protein– protein interaction (PPI) network. Conclusions: This study indicated that the CFS method is a useful tool to identify key genes in glioblastomas. In addition, we also predicted that genes such as PPP2R2B and CYBB might be potential biomarkers for the diagnosis of glioblastomas.

scholarly journals ON THE HEIGHT AND RELATIONAL COMPLEXITY OF A FINITE PERMUTATION GROUP

2021 ◽  
pp. 1-40
Author(s):  
NICK GILL ◽  
BIANCA LODÀ ◽  
PABLO SPIGA
Keyword(s):  
Permutation Group ◽  
Model Theory ◽  
Independent Set ◽  
Maximum Size ◽  
Proper Subset ◽  
Permutation Groups ◽  
Finite Permutation Group ◽  
Pointwise Stabilizer ◽  
Relational Complexity

Abstract Let G be a permutation group on a set $\Omega $ of size t. We say that $\Lambda \subseteq \Omega $ is an independent set if its pointwise stabilizer is not equal to the pointwise stabilizer of any proper subset of $\Lambda $ . We define the height of G to be the maximum size of an independent set, and we denote this quantity $\textrm{H}(G)$ . In this paper, we study $\textrm{H}(G)$ for the case when G is primitive. Our main result asserts that either $\textrm{H}(G)< 9\log t$ or else G is in a particular well-studied family (the primitive large–base groups). An immediate corollary of this result is a characterization of primitive permutation groups with large relational complexity, the latter quantity being a statistic introduced by Cherlin in his study of the model theory of permutation groups. We also study $\textrm{I}(G)$ , the maximum length of an irredundant base of G, in which case we prove that if G is primitive, then either $\textrm{I}(G)<7\log t$ or else, again, G is in a particular family (which includes the primitive large–base groups as well as some others).

scholarly journals Parametric Matroid of Rough Set

2015 ◽  
Vol 23 (06) ◽  
pp. 893-908 ◽  
Author(s):  
Yanfang Liu ◽  
Hong Zhao ◽  
William Zhu
Keyword(s):  
Rough Set ◽  
Equivalence Relation ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Attribute Reduction ◽  
Independent Set ◽  
Approximation Operator ◽  
Approximation Number ◽  
Lower Approximation ◽  
The One

Rough set is mainly concerned with the approximations of objects through an equivalence relation on a universe. Matroid is a generalization of linear algebra and graph theory. Recently, a matroidal structure of rough sets is established and applied to the problem of attribute reduction which is an important application of rough set theory. In this paper, we propose a new matroidal structure of rough sets and call it a parametric matroid. On the one hand, for an equivalence relation on a universe, a parametric set family, with any subset of the universe as its parameter, is defined through the lower approximation operator. This parametric set family is proved to satisfy the independent set axiom of matroids, therefore a matroid is generated, and we call it a parametric matroid of the rough set. Through the lower approximation operator, three equivalent representations of the parametric set family are obtained. Moreover, the parametric matroid of the rough set is proved to be the direct sum of a partition-circuit matroid and a free matroid. On the other hand, partition-circuit matroids are well studied through the lower approximation number, and then we use it to investigate the parametric matroid of the rough set. Several characteristics of the parametric matroid of the rough set, such as independent sets, bases, circuits, the rank function and the closure operator, are expressed by the lower approximation number.

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