Need a way to find matches between two many-to-many-relationships

Question

Given the following tables:

   ------------     ------------
   |     BA   |     |    CA    | 
   ------+-----     ------+-----
   | BId|| AId|     | CId|| AId|
         


        

Answer 1

The number of elements can be calculated using a CTE for CA and BA. Then you can get at the full rows via:

SQL

with ca_info as (
      select
           cid
         , count(*) as ccount
        from ca
      group by cid
  ),
ba_info as (
      select
           bid
         , count(*) as bcount
        from ba
      group by bid
  )
select
*
from
    ba
    join ca on (ba.aid = ca.aid)
    join ba_info on ba.bid=ba_info.bid
    join ca_info on ca.cid=ca_info.cid
where ccount = bcount

SQL Fiddle

Results

bid     aid     cid     aid     bid     bcount  cid     ccount
B1      2       C2      2       B1      2       C2      2
B1      3       C2      3       B1      2       C2      2

If you are just interested in C2 itself, you can restrict the result set more:

with ca_info as (
      select
           cid
         , count(*) as ccount
        from ca
      group by cid
  ),
ba_info as (
      select
           bid
         , count(*) as bcount
        from ba
      group by bid
  )
select
distinct ca.cid
from
    ba
    join ca on (ba.aid = ca.aid)
    join ba_info on ba.bid=ba_info.bid
    join ca_info on ca.cid=ca_info.cid
where ccount = bcount

Supersets

To also get sub/supersets, the condition enforcing the set-equality can be changed:

where ccount <= bcount

This returns all sets where Bx as at least as many elements as Cy:

bid    aid    cid    aid    bid    bcount    cid    ccount
B1     2      C1     2      B1     2          C1    1
B1     2      C2     2      B1     2          C2    2
B1     3      C2     3      B1     2          C2    2
B2     2      C1     2      B2     3          C1    1
B2     2      C2     2      B2     3          C2    2
B2     4      C3     4      B2     3          C3    2
B2     5      C3     5      B2     3          C3    2