Using SPQR-trees to speed up recognition algorithms based on 2-cutsets
Several well-studied classes of graphs admit structural characterizations via proper 2-cutsets which lead to polynomial-time recognition algorithms. The algorithms so far obtained for those recognition problems do not guarantee linear-time complexity. The bottleneck to those algorithms is the Ω(nm)-...
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Veröffentlicht in: | Discrete Applied Mathematics 2018-08, Vol.245, p.101-108 |
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Sprache: | eng |
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Zusammenfassung: | Several well-studied classes of graphs admit structural characterizations via proper 2-cutsets which lead to polynomial-time recognition algorithms. The algorithms so far obtained for those recognition problems do not guarantee linear-time complexity. The bottleneck to those algorithms is the Ω(nm)-time complexity to fully decompose by proper 2-cutsets a graph with n vertices and m edges. In the present work, we investigate the 3-connected components of a graph and propose the use of the SPQR-tree data structure to obtain a fully decomposed graph in linear time. As a consequence, we show that the recognition of chordless graphs and of graphs that do not contain a propeller as a subgraph can be done in linear time, answering questions in the existing literature. |
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ISSN: | 0166-218X 1872-6771 |
DOI: | 10.1016/j.dam.2017.01.009 |