#19197: LatticePoset: add breadth()
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Reporter: jmantysalo | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.9
Component: combinatorics | Resolution:
Keywords: | Merged in:
Authors: Jori Mäntysalo | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/jmantysalo/latticeposet__add_breadth__|
33610ad2c4327679b8dfc1d3af445fe4d9080e4a
Dependencies: | Stopgaps:
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Comment (by ncohen):
Hello,
> For me the parameter name `distance` feels very clear.
And it is not the graph-theoretic distance in the graph, right? Plus there
may be vertices at distance 2 from your start vertex that *never* get
explored because you set distance=3. Do we also agree there? This is due
to the fact that a vertex is at 'distance' k from the source vertex in a
DFS if "there exists a path of length k from the source vertex to it"
(possibly a *very long* path) and that if this vertex is once discovered
at 'distance' 10 000 it may not be 'rediscovered' again at distance 2.
> Why? Doesn't it use more memory?
no reason to. It may be trigger additional copies of the 'queue' list
(unless we implement a deque), but that's all. Additionally, if this cost
worries you then you probably shouldn't use list-comprehension in your
code `:-P`
> I am not sure about that. If I am right, it will make all 2-element
antichains, then all 3-element antichains and so on. There will be many of
them, only one is needed. (But the one must be the right one, of
course...)
With your algorithm: if the antichain {a,b,c} is not "locally minimal",
then your code will test all antichains which contain the antichain
{a,b,c} too. With `subset_with_hereditary_property` it would be filtered
out.
Nathann
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Ticket URL: <http://trac.sagemath.org/ticket/19197#comment:17>
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