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Como obter o pai dado um filho no SQL SERVER 2005


Eu acho que você deve renomear seu child_id para node, seu parent_id para child_of. A nomenclatura da sua coluna está um pouco confusa
create table stack_overflow
(
node int, child_of int
);


insert into stack_overflow(node, child_of) values
(1,0),
(2,1),
(3,2),
(4,2),
(5,3),
(6,4),
(7,0),
(8,7),
(9,8),
(10,1);

Isso funciona em qualquer RDBMS compatível com CTE :
with find_parent(parent, child_of, recentness) as
(
    select node, child_of, 0 
    from stack_overflow
    where node = 9
    union all
    select i.node, i.child_of, fp.recentness + 1
    from stack_overflow i
    join find_parent fp on i.node = fp.child_of
)
select top 1 parent from find_parent 
order by recentness desc

Resultado:
parent
7

[EDIT:mais flexível e à prova de futuro] :
with find_parent(node_group, parent, child_of, recentness) as
(
    select node, node, child_of, 0
    from stack_overflow
    where node in (5,9)
    union all
    select fp.node_group, i.node, i.child_of, fp.recentness + 1
    from stack_overflow i
    join find_parent fp on i.node = fp.child_of
)
select q.node_group as to_find, parent as found 
from find_parent q 
join
(
    select node_group, max(recentness) as answer
    from find_parent
    group by node_group 
) as ans on q.node_group = ans.node_group and q.recentness = ans.answer 
order by to_find    

Resultado:
to_find     found
5           1
9           7

Se você estiver usando o Postgres , o código acima pode ser reduzido para:
with recursive find_parent(node_group, parent, child_of, recentness) as
(
    select node, node, child_of, 0
    from stack_overflow
    where node in (5,9)
    union all
    select fp.node_group, i.node, i.child_of, fp.recentness + 1
    from stack_overflow i
    join find_parent fp on i.node = fp.child_of
)
select distinct on (node_group) node_group as to_find, parent as found 
from find_parent 
order by to_find, recentness desc

DISTINTO nas rochas! :-)