#17537: The geodetic closure of a graph
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Reporter: azi | Owner:
Type: enhancement | Status: needs_info
Priority: minor | Milestone: sage-6.5
Component: graph theory | Resolution:
Keywords: | Merged in:
Authors: Jernej Azarija | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/azi/geodeticClosure | 04f03328e877d2c35ee52228ffde216ae8cb262e
Dependencies: | Stopgaps:
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Comment (by azi):
Replying to [comment:5 ncohen]:
> Hmmm... Calling "distances_all_pairs" in a function like that is a
suicide. You cannot re-compute all distances every time you want to
compute a closure. Actually, the information that you need is precisely
the one that is stored in `convexity_properties`.
That's true, though we can make for an optional argument DP that lets you
pass the distance dictionary in case *anyone* really needs to compute this
often.
>
> The "convexity properties" object associates to every pair of vertices
`u,v` the bitset of all z such that z is on a shortest uv path. Thus if
you need to find the closure of a set of points, all you have to do is
compute the union (with 'or' processor operations) of the bitsets
associated to all pairs of vertices.
I see.
>
> My point is that the code is already there, but of course the name
'convexity properties' is very ill-chosen in this case. We will probably
have to change the terminology... What do you think about all this ?
Fine to me. As far as my preferences go I'd like convexity properties to
be part of the graph/generic graph family and cache this stuff in some
other way. Having a module like that for just a few functions seems a bit
unnatural to me?
>
> By the way, is the terminology 'closure' used anywhere ? Because
formally it is not a closure function. One of the property of closure
functions is that `f(f(X))` should be equal to `f(x)`.
Yes it appears that this is the standard way to call it. See for example
the paper "On pitfalls in computing the geodetic number of a graph" by
Hansen and van Omme.
>
> Nathann
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Ticket URL: <http://trac.sagemath.org/ticket/17537#comment:6>
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