HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Reports

Partially Complemented Representations of Digraphs

Elias Dahlhaus Jens Gustedt 1 Ross M. Mcconnell
1 RESEDAS - Software Tools for Telecommunications and Distributed Systems
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
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 equivalen- ce 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-li- st 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 \omega(m \log n) arcs.
Document type :
Reports
Complete list of metadata

https://hal.inria.fr/inria-00072825
Contributor : Rapport de Recherche Inria Connect in order to contact the contributor
Submitted on : Wednesday, May 24, 2006 - 11:03:02 AM
Last modification on : Friday, February 4, 2022 - 3:30:56 AM
Long-term archiving on: : Sunday, April 4, 2010 - 11:23:52 PM

Identifiers

  • HAL Id : inria-00072825, version 1

Collections

Citation

Elias Dahlhaus, Jens Gustedt, Ross M. Mcconnell. Partially Complemented Representations of Digraphs. [Research Report] RR-3832, INRIA. 1999, pp.24. ⟨inria-00072825⟩

Share

Metrics

Record views

71

Files downloads

105