# Discrete Mathematics & Theoretical Computer Science

## Volume 5 n° 1 (2002), pp. 147-168

author: | Elias Dahlhaus and Jens Gustedt and Ross M. McConnell |
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title: | Partially Complemented Representations of Digraphs |

keywords: | efficient graph algorithms, data structures, search strategies, modular decomposition |

abstract: | A complementation operation on a vertex of a digraph changes all outgoing arcs into non-arcs, and outgoing non-arcs into arcs. This defines an equivalence
relation where two digraphs are equivalent if one can be obtained from
the other by a sequence of such operations. We show that given an
adjacency-list representation of a digraph G, many fundamental
graph algorithms can be carried out on any member G' of G's equivalence
class in O(n+m) time, where m is the number of arcs in G,
not the number of arcs in G' . This may have advantages when
G' is much larger than G. We use this to generalize to digraphs
a simple O(n + m log n) algorithm of McConnell and Spinrad for
finding the modular decomposition of undirected graphs. A key
step is finding the strongly-connected components of a digraph F in G's
equivalence class, where F may have ~(m log n) arcs.
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reference: | Elias Dahlhaus and Jens Gustedt and Ross M. McConnell (2002),
Partially Complemented Representations of Digraphs,
Discrete Mathematics and Theoretical Computer Science 5, pp. 147-168 |

bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |

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Automatically produced on Fri Jun 7 18:19:20 CEST 2002 by gustedt