#16391: Helper functions for OA constructions
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Reporter: ncohen | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.3
Component: combinatorial | Resolution:
designs | Merged in:
Keywords: | Reviewers:
Authors: Nathann Cohen | Work issues:
Report Upstream: N/A | Commit:
Branch: u/ncohen/16391 | 2090875de8a5d9a0301a85fc35e0e60a068de1ab
Dependencies: #16370 | Stopgaps:
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Comment (by ncohen):
Yo !
> I do not want you to remove it but I do not want to see code or doctests
that depend on the lucky case 3). Which implies that you should not use `k
> 3` anywhere.
....
So I can implement it but I am forbidden to use it ?...
Look at what you are doing : you are telling me that it is very bad that
in the future some OA with holes may not exist anymore, for the very same
reason that in the future some OA with holes may become available.
Because we may change constructions, and because if a change can occur in
one direction it can occur in the other direction too.
So the problem is that the "performance may change" in the future, and in
both directions. And more importanty that a doctest may be broken because
somebody ADDS a construction of an OA we were already able to build, which
should not have any effect...
Look man, I have no way around that. I am quite ready to accept that
adding a construction may destroy another whose existence could not be
proved formally, because this thing is useful for a lot of stuff.
And that, again, I have no way around.
And that it only returns true results anyway.
It is a heuristic. It returns true things, but it may not always find
them.
> In the current ticket this function is not used at all, so... Where this
code is merged with #16391?
#16391 is the ticket on which we are talking, so I guess you talk about
#16361. And the ticket which makes #16361 use this helper function is
Wilson's construction #16347. I gave you the updated version of that code
in my last comment on #16361.
> Is there a way to find the largest set of disjoint blocks?
Well, this is precisely what this function does. It solves a maximum
independent set problem on the intersection graph. On a specific OA of
course.
If you want to know if theory knows what the largest set of disjoint
blocks for any k,n I expect that the answer is no. If there exists an
OA(k+1,n) there there exists an OA(k,n)-n.OA(k,1) but it is apparently not
an equivalence.
Nathann
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Ticket URL: <http://trac.sagemath.org/ticket/16391#comment:11>
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