Partitioning sparse graphs into an independent set and a graph with bounded size components

Given a graph [Formula: see text] and an independent set [Formula: see text] of [Formula: see text], the 0–1 inverse maximum independent set problem (IMIS[Formula: see text]) is to delete as few vertices as possible such that [Formula: see text] becomes a maximum independent set of [Formula: see text]. It is known that IMIS[Formula: see text] is NP-hard even when the given independent set has a bounded size. In this paper, we present linear-time algorithms for IMIS[Formula: see text] on forests and unicyclic graphs.

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Approximation algorithms for the weighted independent set problem in sparse graphs

Discrete Applied Mathematics ◽

10.1016/j.dam.2008.08.027 ◽

2009 ◽

Vol 157 (4) ◽

pp. 617-626 ◽

Cited By ~ 11

Author(s):

Akihisa Kako ◽

Takao Ono ◽

Tomio Hirata ◽

Magnús M. Halldórsson

Keyword(s):

Approximation Algorithms ◽

Independent Set ◽

Sparse Graphs ◽

Independent Set Problem

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Partitioning Sparse Graphs into an Independent Set and a Forest of Bounded Degree

The Electronic Journal of Combinatorics ◽

10.37236/6815 ◽

2018 ◽

Vol 25 (1) ◽

Author(s):

François Dross ◽

Mickael Montassier ◽

Alexandre Pinlou

Keyword(s):

Planar Graphs ◽

Maximum Degree ◽

Independent Set ◽

Average Degree ◽

Bounded Degree ◽

Sparse Graphs ◽

Maximum Average Degree

An $({\cal I},{\cal F}_d)$-partition of a graph is a partition of the vertices of the graph into two sets $I$ and $F$, such that $I$ is an independent set and $F$ induces a forest of maximum degree at most $d$. We show that for all $M<3$ and $d \ge \frac{2}{3-M} - 2$, if a graph has maximum average degree less than $M$, then it has an $({\cal I},{\cal F}_d)$-partition. Additionally, we prove that for all $\frac{8}{3} \le M < 3$ and $d \ge \frac{1}{3-M}$, if a graph has maximum average degree less than $M$ then it has an $({\cal I},{\cal F}_d)$-partition. It follows that planar graphs with girth at least $7$ (resp. $8$, $10$) admit an $({\cal I},{\cal F}_5)$-partition (resp. $({\cal I},{\cal F}_3)$-partition, $({\cal I},{\cal F}_2)$-partition).

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Ramsey-type theorems for lines in 3-space

Discrete Mathematics & Theoretical Computer Science ◽

10.46298/dmtcs.1367 ◽

2016 ◽

Vol Vol. 18 no. 3 (Combinatorics) ◽

Author(s):

Jean Cardinal ◽

Michael S. Payne ◽

Noam Solomon

Keyword(s):

Lower Bounds ◽

Polynomial Time ◽

General Position ◽

Independent Set ◽

Independent Sets ◽

Intersection Graph ◽

Sparse Graphs ◽

Polynomial Time Algorithms ◽

Ramsey Type ◽

Point Line

We prove geometric Ramsey-type statements on collections of lines in 3-space. These statements give guarantees on the size of a clique or an independent set in (hyper)graphs induced by incidence relations between lines, points, and reguli in 3-space. Among other things, we prove that: (1) The intersection graph of n lines in R^3 has a clique or independent set of size Omega(n^{1/3}). (2) Every set of n lines in R^3 has a subset of n^{1/2} lines that are all stabbed by one line, or a subset of Omega((n/log n)^{1/5}) such that no 6-subset is stabbed by one line. (3) Every set of n lines in general position in R^3 has a subset of Omega(n^{2/3}) lines that all lie on a regulus, or a subset of Omega(n^{1/3}) lines such that no 4-subset is contained in a regulus. The proofs of these statements all follow from geometric incidence bounds -- such as the Guth-Katz bound on point-line incidences in R^3 -- combined with Tur\'an-type results on independent sets in sparse graphs and hypergraphs. Although similar Ramsey-type statements can be proved using existing generic algebraic frameworks, the lower bounds we get are much larger than what can be obtained with these methods. The proofs directly yield polynomial-time algorithms for finding subsets of the claimed size. Comment: 18 pages including appendix

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An O *(1.0977 n ) Exact Algorithm for max independent set in Sparse Graphs

Parameterized and Exact Computation - Lecture Notes in Computer Science ◽

10.1007/978-3-540-79723-4_7 ◽

2008 ◽

pp. 55-65 ◽

Cited By ~ 8

Author(s):

Nicolas Bourgeois ◽

Bruno Escoffier ◽

Vangelis Th. Paschos

Keyword(s):

Independent Set ◽

Exact Algorithm ◽

Sparse Graphs

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A genetic algorithm-based heuristic for solving the weighted maximum independent set and some equivalent problems

Journal of the Operational Research Society ◽

10.1038/sj.jors.2600405 ◽

1997 ◽

Vol 48 (6) ◽

pp. 612-622 ◽

Cited By ~ 11

Author(s):

M Hifi

Keyword(s):

Genetic Algorithm ◽

Independent Set ◽

Maximum Independent Set ◽

Equivalent Problems

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Prediction of K562 Cells Functional Inhibitors Based on Machine Learning Approaches

Current Pharmaceutical Design ◽

10.2174/1381612825666191107092214 ◽

2020 ◽

Vol 25 (40) ◽

pp. 4296-4302 ◽

Cited By ~ 2

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.

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

Current Bioinformatics ◽

10.2174/1574893615999200819162140 ◽

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.

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