An improved parameterized algorithm for the p-cluster vertex deletion problem View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2015-10-23

AUTHORS

Bang Ye Wu, Li-Hsuan Chen

ABSTRACT

In the p-Cluster Vertex Deletion problem, we are given a graph G=(V,E)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G=(V,E)$$\end{document} and two parameters k and p, and the goal is to determine if there exists a subset X of at most k vertices such that the removal of X results in a graph consisting of exactly p disjoint maximal cliques. Let r=p/k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r=p/k$$\end{document}. In this paper, we design a branching algorithm with time complexity O(αk+|V||E|)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(\alpha ^k+|V||E|)$$\end{document}, where α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} depends on r and has a rough upper bound min{1.6181+r,2}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\min \{1.618^{1+r},2\}$$\end{document}. With a more precise analysis, we show that α=1.28·3.57r\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha =1.28\cdot 3.57^{r}$$\end{document} for r≤0.219\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r\le 0.219$$\end{document}; α=(1-r)r-1r-r\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha =(1-r)^{r-1}r^{-r}$$\end{document} for 0.219 More... »

PAGES

373-388

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10878-015-9969-4

DOI

http://dx.doi.org/10.1007/s10878-015-9969-4

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1027437306


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