#17921: faster matching polynomial
-------------------------------------+-------------------------------------
Reporter: pernici | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.6
Component: graph theory | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/pernici/ticket/17921 | fe2fa06af8efa606d4bbd6256336c11a93da9a32
Dependencies: | Stopgaps:
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Changes (by pernici):
* cc: vdelecroix (added)
* commit: => fe2fa06af8efa606d4bbd6256336c11a93da9a32
Old description:
> ADD DESCRIPTION
>
> Added ``matching_generating_poly``, modified ``matching_polynomial``
>
> ``matching_generating_poly`` computes the matching generating polynomial
> on (possibly weighted) graphs.
>
> The algorithm (see [ButPer]) uses polynomials on nilpotent elements,
> implemented in the class ``Hobj`` in matchpoly.pyx,
> and a greedy argument to order edges, contained in active_nodes.py
>
> This algorithm is faster than the Godsil algorithm on large graphs.
New description:
ADD DESCRIPTION
Added ``matching_generating_poly``, modified ``matching_polynomial``,
added an option
to ``permanental_minor_polynomial``, which for some graphs is faster than
the previous
algorithm.
``matching_generating_poly`` computes the matching generating polynomial
on (possibly weighted) graphs; this is used in
``permanental_minor_polynomial``.
The algorithm (see [ButPer]) uses polynomials on nilpotent elements,
implemented in the class ``Hobj`` in matchpoly.pyx,
and a greedy argument to order edges, contained in active_nodes.py
This algorithm is much faster than the Godsil algorithm on large graphs.
``
sage: from sage.graphs.matchpoly import matching_generating_poly
sage: g = graphs.BuckyBall()
sage: time sum(matching_generating_poly(g).coefficients())
CPU times: user 184 ms, sys: 0 ns, total: 184 ms
Wall time: 184 ms
1417036634543488
``
--
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Ticket URL: <http://trac.sagemath.org/ticket/17921#comment:2>
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