#12743: Addition of reduction rules as pre-processing of the vertex cover
function
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Reporter: dcoudert | Owner: jason, ncohen, rlm
Type: enhancement | Status: new
Priority: major | Milestone: sage-5.0
Component: graph theory | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: David Coudert | Merged in:
Dependencies: | Stopgaps:
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Description changed by dcoudert:
Old description:
> This patch adds basic reduction rules as a pre-processing of the vertex
> cover function. These reduction rules are the 3 first rules described for
> instance in
> http://people.scs.carleton.ca/~dehne/projects/clustalxp/ACFLSS.pdf, that
> is: (1) vertices of degree 0 are not part of the cover, (2) the neighbor
> of a vertex of degree 1 is in the cover, and (3) if the neighbors of a
> degree 2 vertex are incident, they are in the cover.
>
> This is particularly useful for sparse graphs.
>
> More advanced reduction rules can also be considered (crown
> decompositions, etc.) but are not part of this patch.
New description:
This patch adds basic reduction rules as a pre-processing of the vertex
cover function. These reduction rules are the 3 first rules described for
instance in
http://people.scs.carleton.ca/~dehne/projects/clustalxp/ACFLSS.pdf, that
is:
1. vertices of degree 0 are not part of the cover
1. the neighbor of a vertex of degree 1 is in the cover
1. if the neighbors of a degree 2 vertex are incident, they are in the
cover
1. if the two neighbors v,w of a degree 2 vertex u are not incident, then
either u is in the cover or v and w are in the cover.
This is particularly useful for sparse graphs.
More advanced reduction rules can also be considered (crown
decompositions, etc.) but are not part of this patch.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12743#comment:1>
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