# Re: how to suppress carefully a recursive tree

From: fj <francois.jacq_at_irsn.fr>
Date: Tue, 22 Jan 2008 08:10:35 -0800 (PST)

On 22 jan, 15:52, Jan Hidders <hidd..._at_gmail.com> wrote:
> On 22 jan, 12:04, fj <francois.j..._at_irsn.fr> wrote:
>
> > I know how to suppress a normal tree but I meet the following kind of
> > situation :
>
> I'm guessing that when you say "suppress" you mean "represent in a
> database". Correct?

>
>
>
> > r1
> > -> b1
> > -> b2 -> ...
> > -> b3 -> ...
> > -> b2
> > -> b1 -> ...
> > -> b1 -> ...
> > -> b3
> > -> b4
>
> > r2
> > -> b3 -> ...
>
> So, a directed graph with multiple roots. Correct? So basically you
> want to store arbitrary directed graphs.

Yes and no. The two "roots" r1 r2 could perhaps belong to a bigger tree.

>
> > A same node can be referenced at several places. Each node is
> > associated to a storage count :
>
> > r1(0) b1(3) b2(2) b3(3) b4(1) r2(0)
>
> Which would correspond to the number of incoming edges, yes?

Yes

>
> > In a normal tree without recursion (in the example above, recursion
> > occurs because b1 contains b2 and vice versa), a node is destroyed
> > when its count storage is equal to zero else its count storage is
> > simply decremented.
>
> > What algorithm should be applied ? I want for instance to cleanup r1
> > but, of course, r2 must remain valid (=> b3 and b4 are not destroyed
> > during the process and their storage count must be b3(1) b4(1)).
>
> > Notice that the deletion of of a tree must be possible even if the
> > count storage of the root is not equal to zero :
> > r1 -> b1 -> b2 -> r1 -> ...
>
> It all depends a bit on how large your typical graphs are, how long on
> average the simple paths, what type of operations and queries you want
> to do on it and how often. My first guess for the representation
> would a simple straightforward adjacency list representation, (a
> binary relation that contains all the edges) and if it's not too big
> and your paths are often long it might be interesting to maintain an
> extra table with the transitive closure of the graph.

The graph may be quite large. Number of vertices (nodes) : usually 100000, sometimes much more (a very big computation may lead to about 100 millions). This corresponds to a 3D meshing, each mesh (a particular node) containing information about chemical composition (a sub-node), temperature, fluid characteristics (another sub-node) ...

Let us precise that simple paths are always short when one excludes recursive points (a maximum of 10 nodes).

> If you go for the adjacency list approach, make sure that you do as
> much as possible in one SQL statement when you start following the
> edges. So look up all nodes that are reachable in one step in one
> statement, update those, and store the ones that have to be deleted in
> a temporary table. Then again with one statement look up those that
> can be reached from in one step from the nodes in the temporary table.
> Et cetera.

A short cut would be to store the external counts in the nodes themselves but, unfortunately, this is (more or less) forbidden : the data base needs to work in a // environment (openMP) and two simultaneous calls to the deletion routine with two trees sharing data could lead to crashing the application. Anyway, this solution will be adopted if I don't find a better algorithm (the deletion routine will be protected by a semaphore blocking other threads wanting to destroy something).

I just wanted to know if a better algorithm was available. The problem is more or less connected to garbage collector techniques. Python language should have the same trouble when trying to destroy a dictionary (variables of a dictionary may belong to another dictionary).

>
> Does that help?
>
> PS. Expect a shameless but informative plug by Joe Celko for one of
> his books. :-)
>
> -- Jan Hidders
Received on Tue Jan 22 2008 - 17:10:35 CET

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