Tsql – Multiple parents tree (or digraph) implementation sql server 2005

hierarchyparent-childsql-server-2005treetsql

I need to implement a multi-parented tree (or digraph) onto SQL Server 2005.
I've read several articles, but most of them uses single-parented trees with a unique root like the following one.

-My PC
   -Drive C
      -Documents and Settings
      -Program Files
         -Adobe
         -Microsoft
      -Folder X
   -Drive D
      -Folder Y
      -Folder Z

In this one, everything derives from a root element (My PC).

In my case, a child could have more than 1 parent, like the following:

G  A
 \ /
  B
 / \ 
X   C
  /  \
  D   E
  \ /
   F

So I have the following code:

create table #ObjectRelations
(
    Id varchar(20),
    NextId varchar(20)
)

insert into #ObjectRelations values ('G', 'B')
insert into #ObjectRelations values ('A', 'B') 
insert into #ObjectRelations values ('B', 'C')
insert into #ObjectRelations values ('B', 'X')
insert into #ObjectRelations values ('C', 'E') 
insert into #ObjectRelations values ('C', 'D') 
insert into #ObjectRelations values ('E', 'F') 
insert into #ObjectRelations values ('D', 'F') 

declare @id varchar(20)
set @id = 'A';

WITH Objects (Id, NextId) AS
( -- This is the 'Anchor' or starting point of the recursive query
  SELECT rel.Id,
         rel.NextId
    FROM #ObjectRelations rel
   WHERE rel.Id = @id
   UNION ALL -- This is the recursive portion of the query
  SELECT rel.Id,
         rel.NextId
    FROM #ObjectRelations rel
   INNER JOIN Objects -- Note the reference to CTE table name (Recursive Join)
      ON rel.Id = Objects.NextId
)
SELECT  o.*
FROM    Objects o

drop table #ObjectRelations

Which returns the following SET:

Id                   NextId
-------------------- --------------------
A                    B
B                    C
B                    X
C                    E
C                    D
D                    F
E                    F

Expected result SET:

Id                   NextId
-------------------- --------------------
G                    B
A                    B
B                    C
B                    X
C                    E
C                    D
D                    F
E                    F

Note that the relation G->B is missing, because it asks for an starting object (which doesn't work for me also, because I don't know the root object from the start) and using A as the start point will ignore the G->B relationship.

So, this code doesn't work in my case because it asks for a starting object, which is obvious in a SINGLE-parent tree (will always be the root object). But in multi-parent tree, you could have more than 1 "root" object (like in the example, G and A are the "root" objects, where root is an object which doesn't have a parent (ancestor)).

So I'm kind of stucked in here… I need to modify the query to NOT ask for a starting object and recursively traverse the entire tree.
I don't know if that's possible with the (Id, NextId) implementation… may be I need to store it like a graph using some kind of Incidence matrix, adjacency matrix or whatever (see http://willets.org/sqlgraphs.html).

Any help? What do you think guys?
Thank you very much for your time =)

Cheers!

Sources:
Source 1
Source 2
Source 3

Best Solution

Well, I finally came up with the following solution. It's the way I found to support multi-root trees and also cycling digraphs.

create table #ObjectRelations
(
    Id varchar(20),
    NextId varchar(20)
)

/* Cycle */
/*
insert into #ObjectRelations values ('A', 'B')
insert into #ObjectRelations values ('B', 'C') 
insert into #ObjectRelations values ('C', 'A')
*/

/* Multi root */

insert into #ObjectRelations values ('G', 'B')
insert into #ObjectRelations values ('A', 'B') 
insert into #ObjectRelations values ('B', 'C')
insert into #ObjectRelations values ('B', 'X')
insert into #ObjectRelations values ('C', 'E') 
insert into #ObjectRelations values ('C', 'D') 
insert into #ObjectRelations values ('E', 'F') 
insert into #ObjectRelations values ('D', 'F') 


declare @startIds table
(
    Id varchar(20) primary key
)

;WITH 
    Ids (Id) AS
    (
        SELECT  Id
        FROM    #ObjectRelations
    ),
    NextIds (Id) AS
    (
        SELECT  NextId
        FROM    #ObjectRelations
    )
INSERT INTO @startIds
/* This select will not return anything since there are not objects without predecessor, because it's a cyclic of course */
SELECT DISTINCT
    Ids.Id
FROM
    Ids
LEFT JOIN
    NextIds on Ids.Id = NextIds.Id
WHERE
    NextIds.Id IS NULL
UNION
/* So let's just pick anyone. (the way I will be getting the starting object for a cyclic doesn't matter for the regarding problem)*/
SELECT TOP 1 Id FROM Ids

;WITH Objects (Id, NextId, [Level], Way) AS
( -- This is the 'Anchor' or starting point of the recursive query
  SELECT rel.Id,
         rel.NextId,
         1,
         CAST(rel.Id as VARCHAR(MAX))
    FROM #ObjectRelations rel
   WHERE rel.Id IN (SELECT Id FROM @startIds)

   UNION ALL -- This is the recursive portion of the query

  SELECT rel.Id,
         rel.NextId,
         [Level] + 1,
         RecObjects.Way + ', ' + rel.Id
    FROM #ObjectRelations rel
   INNER JOIN Objects RecObjects -- Note the reference to CTE table name (Recursive Join)
      ON rel.Id = RecObjects.NextId
   WHERE RecObjects.Way NOT LIKE '%' + rel.Id + '%'

)
SELECT  DISTINCT 
        Id,
        NextId,
        [Level]
FROM    Objects
ORDER BY [Level]

drop table #ObjectRelations

Could be useful for somebody. It is for me =P Thanks