Recognition of Probe Cographs and Partitioned Probe Distance Hereditary Graphs View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2006

AUTHORS

David B. Chandler , Maw-Shang Chang , Ton Kloks , Jiping Liu , Sheng-Lung Peng

ABSTRACT

Given a class of graphs \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\cal G}$\end{document}, a graph G is a probe graph of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\cal G}$\end{document} if its vertices can be partitioned into two sets ℙ (the probes) and ℕ (nonprobes), where ℕ is an independent set, such that G can be embedded into a graph of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\cal G}$\end{document} by adding edges between certain vertices of ℕ. If the partition of the vertices into probes and nonprobes is part of the input, then we call the graph a partitioned probe graph of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\cal G}$\end{document}. We give the first polynomial-time algorithm for recognizing partitioned probe distance-hereditary graphs. By using a novel data structure for storing a multiset of sets of numbers, the running time of this algorithm is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${O}(\mathfrak\it{n}^2)$\end{document}, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathfrak\it{n}$\end{document} is the number of vertices of the input graph. We also show that the recognition of both partitioned and unpartitioned probe cographs can be done in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${O}(\mathfrak\it{n}^2)$\end{document} time. More... »

PAGES

267-278

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/11775096_25

DOI

http://dx.doi.org/10.1007/11775096_25

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1028368901


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