Comments (3)
@anfelor Yes!
In fact, this graph composition will also allow us to implement an instance of Dioid
for labelled graphs, much like this is usually done with matrices whose elements are dioids. We will use |*| = compose
.
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In the labelled graph setting, would the relational composition use the multiplication of our dioid
e. g. (a [ l ]> b) * (b [ k ]> c) = a [ l * k ]> c
?
from alga.
#148 provides an implementation of relational composition of algebraic graphs. Note that it is not as good as I hoped for: the size of the resulting expression is O(m1+m2), where m1 and m2 are the number of edges in the given graphs. Note however that the number of edges in the resulting graph may be quadratic, i.e. O(m1*m2), hence the algebraic representation is still very compact.
The implementation is quite short, the main trick is using biclique
:
compose :: Ord a => Graph a -> Graph a -> Graph a
compose x y = overlays
[ biclique xs ys
| v <- Set.toList (AM.vertexSet mx `Set.union` AM.vertexSet my)
, let xs = Set.toList (AM.postSet v mx), not (null xs)
, let ys = Set.toList (AM.postSet v my), not (null ys) ]
where
mx = toAdjacencyMap (transpose x)
my = toAdjacencyMap y
In combination with graph sparsification, this is quite powerful. I will write a blog post to explain how to combine sparsify
and compose
in an interesting way.
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Related Issues (20)
- How to handle goodness inherited from other libraries HOT 2
- Bump upper bound for base-compat for version 0.4 on Hackage HOT 4
- Unable to use ghcid HOT 6
- Algorithms should be in terms of typeclasses not data structures HOT 15
- Acyclic graphs with Int labels HOT 5
- Tests failed to build with QuickCheck 2.14.2
- Multitree HOT 3
- Monoid instance HOT 6
- support for GraphViz "HTML strings" for node or edge labels HOT 1
- Add benchmarks to CI HOT 2
- Supporting different node and edge types HOT 7
- v0.6 fails to build with GHC 8.0 and 8.2 HOT 3
- Doubt about decorating a Graph HOT 4
- Compatibility with mtl-2.3 HOT 2
- Smart constructor for Symbol rather than requiring -XOverloadedLists HOT 1
- Proposal : foldgM HOT 2
- Algebra.Graph.Labelled.AdjacencyMap.edges appears to be broken HOT 2
- Semigroup version of Algebra.Graph.Labelled.AdjacencyMap HOT 7
- Bump "deepseq" dependency bounds to 1.5.0.0 HOT 2
- Warnings when building with ghc-9.10
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