Re: how to suppress carefully a recursive tree
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?
> > 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.
I don't use SQL but it does not matter : I can build up easily the
list of nodes related to a particular starting point (the node "env"
in my example). I am also able to compute, for each node, its
"external count" (0 for all the nodes except b3 which has the value
After that I can start to destroy really : I only go down the nodes
which have an external count equal to zero (this will protect b4 in
the example). The problem is that the algorithm is not very efficient
when the list of nodes is high, simply because I need, for each node
having a storage count greater than 0, to look for that node in the
list of all the nodes and to check the external count (CPU cost
proportional to O(n2) if n is the number of concerned nodes).
After that I can start to destroy really : I only go down the nodes which have an external count equal to zero (this will protect b4 in the example). The problem is that the algorithm is not very efficient when the list of nodes is high, simply because I need, for each node having a storage count greater than 0, to look for that node in the list of all the nodes and to check the external count (CPU cost proportional to O(n2) if n is the number of concerned nodes).
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