Re: [Caml-list] Poset variant of union-find datastructure

[Christophe Raffalli <raffalli@univ-savoie.fr>]

Le 27/07/2011 22:20, Guillaume Yziquel a écrit :
> Hi.
>
> I'm wondering if people on this list may have any insight as to how
> implement a "poset-find" datastructure much like a union-find
> datastructure.
>
> A typical union find signature can be found here:
>
> http://www.enseignement.polytechnique.fr/informatique/INF564/html/unionFind.mli.html
>
> The core of the signature I'm interested in is:
>
> 	type 'a point
> 	val fresh : 'a -> 'a point
> 	val find : 'a point -> 'a
> 	val union : 'a point -> 'a point -> unit
> 	val equivalent : 'a point -> 'a point -> bool
>
> and I'd like a similar signature like:
>
> 	type 'a point
> 	type rel : G | Geq | Eq | Leq | L
> 	val fresh : 'a -> 'a point
> 	val find : 'a point -> 'a
> 	val relate : rel -> 'a point -> 'a point -> unit
> 	val relation : 'a point -> 'a point -> rel option
>
> Has anybody given thought to this kind of datastructure, or is there any
> prior work? Or is there really no better alternative than a graph? What
> worries me about a graph is that I do not really perceive an efficient way
> to query the order between two 'a points.
>
Hello,
 
I only see the graph solution (unfortunately) ... With variants:

- just a graph, querying the relation requiring to traverse the graph
- computing the transitive closure of the graph (relate taking more time),
but querying being much faster.
- computing both the transitive closure and the transitive reduction of
the grap
which reduce a bit the time for relate (less edges to follow). But not
changing the
worst case complexity, I think.

I would be very happy too if there were a more efficient solution
(logarithmic complexity both for relation and relate ?)

Cheers,
Christophe