Graph/ModularDecomposition version 0.15
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Graph::ModularDecomposition implements finding the modular
decomposition tree of an n-vertex directed graph in O(n^2) time.
Several graph algorithms use the modular decomposition tree as a
building block.
This implementation derives from Graph::Directed, providing additional
methods. To decompose an undirected graph, represent it as a directed
graph: replace each undirected edge by two directed edges.
The code here is based on algorithm 6.1 for modular decomposition of
two-structures, from
A. Ehrenfeucht, H. N. Gabow, R. M. McConnell, and S. J. Sullivan,
"An O(n^2) Divide-and-Conquer Algorithm for the Prime Tree
Decomposition of Two-Structures and Modular Decomposition of
Graphs", Journal of Algorithms 16 (1994), pp. 283-294.
doi:10.1006/jagm.1994.1013
There are O(m+n) time algorithms that perform better for sparse graphs
where the number m of edges is small compared to n^2, see
R. M. McConnell and F. de Montgolfier, "Linear-time modular
decomposition of directed graphs", Discrete Applied Mathematics
145 (2005), pp. 198-209. doi:10.1016/j.dam.2004.02.017
A simple example application of these routines is to construct and
search the modular decomposition tree of a directed graph to decide
if it is node-series-parallel. This can also be done using the
Valdes-Tarjan-Lawler algorithm published in 1982, but the approach
here also yields the modular decomposition tree. The method
classify() uses the modular decomposition tree to classify a
directed graph as non-transitive, or for transitive digraphs, as
series-parallel (linear or parallel modules only), decomposable
(not series-parallel, but with at least one non-primitive module),
indecomposable (primitive), decomposable but consisting of primitive
or series modules only (only applies to graphs of at least 7 vertices),
or unclassified (should never apply).
WARNING: Treat this as alpha quality code. It has only been
tested on small graphs with up to a few dozen vertices.
On a make test, Devel::Cover currently reports the following test
coverage statistics (without Bitvector2 present):
File stmt branch cond sub pod time total
---------------------------- ------ ------ ------ ------ ------ ------ ------
...h/ModularDecomposition.pm 99.7 85.7 74.1 100.0 100.0 100.0 93.8
INSTALLATION
To install this module, do the usual:
perl Makefile.PL
make
make test
make install
DEPENDENCIES
This module is for Perl 5.006 or later (it has been tested on 5.24),
and depends on modules Carp and Exporter. For the Pod tests,
Test::More is required.
Graph::ModularDecomposition is derived from Graph::Directed, which is
part of Jarkko Hietaniemi's Graph module. At least version 0.20105
of Graph is required.
Two routines to convert to Graph::Bitvector2 objects are available if
Graph::Bitvector2 is installed. This module has not yet been released.
COPYRIGHT AND LICENCE
This module is licensed on the same copyright terms as Perl.
Copyright (C) 2004-17 by Andras Salamon