Add RandomLattice method. #175
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reiniscirpons
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I have implemented the requested changes. Could you review if everything is ok? Thanks :) |
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Thanks so much @reiniscirpons, a couple of further minor revisions are required, then I'll be happy for this to be merged.
| UniteSet(fam, List(fam, x -> UnionBlist(x, rand_blist))); | ||
| od; | ||
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| return Digraph(IsMutableDigraph, fam, IsSubsetBlist); |
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| while Length(fam) < n do | ||
| rand_blist := List([1 .. n], x -> Random([true, false])); | ||
| UniteSet(fam, List(fam, x -> UnionBlist(x, rand_blist))); |
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I have no idea if this would make any difference but you could use Set instead of List here.
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Interesting suggestion, I tried it out, but in practice it is a slightly slower or the same with Set, presumably since it needs to reorder the list, which adds time, and then UniteSet does not take advantage of the second argument being a Set.
This makes sense since UniteSet(set, list) is only defined for a set and a list, so I do not think that having a Set instead of a List as the second argument will change the algorithm its using (which I think is to just add each element in the list to the set).
Therefore I will not change it to Set.
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Ok, that all makes sense.
james-d-mitchell
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Thanks @reiniscirpons, merged! |
This PR adds a method
RandomLatticefor constructing random lattices, given a positive integernas input.It then incrementally calculates a union lattice of sets, terminating once the lattice has at least
nvertices. It is guaranteed that the resulting lattice will have at leastnand no more than2*nvertices. The average time complexity seems to beO(n^2).Some results on the distribution of such lattices can be derived from
"The representation of posets and lattices by sets"
George Markowsky
Algebra Universalis, 11 (1980), 173-192