Data.Graph transitive closure

Johannes Waldmann johannes.waldmann at
Fri Jun 21 14:01:03 UTC 2019

> ... reasonably efficient transitive closure for Data.Graph ...

well, since we have

  type Graph = Array Vertex [Vertex]

efficiency is already questionable?
We cannot quickly check whether an edge is present,
we cannot quickly get all predecessors of a vertex.
But perhaps we don't need to. The underlying assumptions
(cost of elementary operations)
are not immediately clear.

The cited Agda library has

   newtype Graph n e = Graph (Map n (Map n e))

Another option is to store back edges as well, as in

FGL fuses these two maps

type GraphRep a b = IntMap (Context' a b)
type Context' a b = (IntMap [b], a, IntMap [b])

this saves some look-ups (if you need successors and
predecessors of the very same node)
but this can't be used for relations,
where start and end of an edge have different types.
But for transitive closure, these types would agree anyway.

What to make of this?

Perhaps Data.Graph should be moved out of containers.
The design space is just too large to single out one specific point?
If we keep it, it would be very nice to document the complexity
of algorithms. Section 7 of the King/Launchbury paper
(cited in the API docs) claims "DFS in O(V+E)", backed up by
experiments. This seems to be the main motivation for this library
(DFS, with application: SCC). It's not clear whether the underlying
design should be recommended for a general graph library.

- Johannes

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