Re: Brain teaser for non-PK tables

* Richard Cyganiak <richard@cyganiak.de> [2012-04-24 21:15+0100]
> So, Eric challenged me to present an example of a query over a direct-mapped PK-less table that I believe cannot be evaluated in standard SQL without materializing the entire table outside of the DB.
> 
> First let me say that I've puzzled over this non-PK issue for more than a day, trying to come up with some scheme based on cursors or ROWNUM or local variables to make it work, and failed. Now, making a leap from “I couldn't do it in a day” to “It's impossible” is certainly not quite appropriate, but after that experience I felt justified to send an implementation experience report to the WG, stating my belief that the cost of implementing this scheme are not worth the benefits. Hence my proposal to let implementers choose whether they want to implement the lean or non-lean direct mapping.
> 
> So here we go.
> 
>           IOU
>    BORROWER | AMOUNT
>    ---------+-------
>    Alice    |     10
>    Bob      |      5
>    Charlie  |     10
>    Charlie  |     10
> 
> The equivalent non-lean direct mapping graph (minus rdf:type triples):
> 
>    _:1 <IOU#BORROWER> "Alice".
>    _:1 <IOU#AMOUNT> 10.
>    _:2 <IOU#BORROWER> "Bob".
>    _:2 <IOU#AMOUNT> 5.
>    _:3 <IOU#BORROWER> "Charlie".
>    _:3 <IOU#AMOUNT> 10.
>    _:4 <IOU#BORROWER> "Charlie".
>    _:4 <IOU#AMOUNT> 10.
> 
> Now here's a simple SPARQL query:
> 
>    SELECT * {
>       {
>          ?x <IOU#BORROWER> "Charlie".
>          ?x ?property ?value.
>       } UNION {
>          ?x <IOU#AMOUNT> 10.
>       }
>    }
> 
> The solution should be:
> 
>    ?x  | ?property      | ?value
>    ----+----------------+----------
>    _:3 | <IOU#BORROWER> | "Charlie"
>    _:4 | <IOU#BORROWER> | "Charlie"
>    _:3 | <IOU#AMOUNT>   | 10
>    _:4 | <IOU#AMOUNT>   | 10
>    _:1 |                |
>    _:3 |                |
>    _:4 |                |
> 
> Can you outline an algorithm that produces this result without materializing the table? (Ordering, the difference between literals/IRIs/bNodes, and the specific labels for the bNodes don't matter.)
> 
> Bonus points if the algorithm is expressed as an R2RML mapping. We can assume that we already have an algorithm for evaluating any SPARQL query over an R2RML mapping.
> 
> Here's my non-standard solution using ROWID, which only works on Oracle:
> 
>   SELECT ROWID x, '<IOU#BORROWER>' property, BORROWER value
>          FROM IOU
>          WHERE BORROWER='Charlie'
>   UNION
>   SELECT ROWID x, '<IOU#AMOUNT>' property, AMOUNT value
>          FROM IOU
>          WHERE BORROWER='Charlie'
>   UNION
>   SELECT ROWID x, NULL, NULL
>          FROM IOU
>          WHERE AMOUNT=10

Oracle insisted that I tweak this to work preserve datatype consistency:

  SELECT ROWID x, '<IOU#BORROWER>' property, BORROWER v1, NULL v2
         FROM IOU
         WHERE BORROWER='Charlie'
  UNION
  SELECT ROWID x, '<IOU#AMOUNT>' property, NULL v1, AMOUNT v2
         FROM IOU
         WHERE BORROWER='Charlie'
  UNION
  SELECT ROWID x, NULL property, NULL v1, NULL v2
         FROM IOU
         WHERE AMOUNT=10;

X     PROPERTY   V1    V2
------------------ -------------- ------- ----------
AAAdX+AAEAAAF0tAAA
AAAdX+AAEAAAF0tAAC <IOU#AMOUNT>     10
AAAdX+AAEAAAF0tAAC <IOU#BORROWER> Charlie
AAAdX+AAEAAAF0tAAC
AAAdX+AAEAAAF0tAAD <IOU#AMOUNT>     10
AAAdX+AAEAAAF0tAAD <IOU#BORROWER> Charlie
AAAdX+AAEAAAF0tAAD

To get rid of ROWID, I selected a counted IOU table with
s/IOU
 /(select BORROWER, AMOUNT, count(*) AS ccc from IOU group by BORROWER, AMOUNT) IOU
 /g

  SELECT BORROWER, AMOUNT, ccc, '<IOU#BORROWER>' property, BORROWER v1, NULL v2
         FROM (select BORROWER, AMOUNT, count(*) AS ccc from IOU group by BORROWER, AMOUNT) IOU
         WHERE BORROWER='Charlie'
  UNION
  SELECT BORROWER, AMOUNT, ccc, '<IOU#AMOUNT>' property, NULL v1, AMOUNT v2
         FROM (select BORROWER, AMOUNT, count(*) AS ccc from IOU group by BORROWER, AMOUNT) IOU
         WHERE BORROWER='Charlie'
  UNION
  SELECT BORROWER, AMOUNT, ccc, NULL property, NULL v1, NULL v2
         FROM (select BORROWER, AMOUNT, count(*) AS ccc from IOU group by BORROWER, AMOUNT) IOU
         WHERE AMOUNT=10;

BORROWE     AMOUNT   CCC PROPERTY      V1       V2
------- ---------- ---------- -------------- ------- ----------
Charlie  10     2 <IOU#BORROWER> Charlie
Charlie  10     2 <IOU#AMOUNT>       10
Alice  10     1
Charlie  10     2

Each row emits CCC solutions where x is bound to a function of the
first three columns iterating i from 1 to CCC, allocating or re-using
a bnode in a hash of lists of bnodes:

Charlie  10     2 <IOU#BORROWER> Charlie
  bnodes{x}{Charlie-10}[1] = _:b
  results += (?x -> _:b, ?property -> <IOU#BORROWER>, ?value -> "Charlie")
  bnodes{x}{Charlie-10}[2] = _:c
  results += (?x -> _:c, ?property -> <IOU#BORROWER>, ?value -> "Charlie")
Charlie  10     2 <IOU#AMOUNT>       10
  results += (?x -> _:b, ?property -> <IOU#AMOUNT>, ?value -> 10)
  results += (?x -> _:c, ?property -> <IOU#AMOUNT>, ?value -> 10)
Alice  10     1
  bnodes{x}{Alice-10}[1] = _:a
  results += (x -> _:a)
Charlie  10     2
  results += (?x -> _:b)
  results += (?x -> _:c)


> Earning the R2RML bonus points:
> 
>    <#map> a rr:TriplesMap;
>       rr:logicalTable [
>          rr:sqlQuery "SELECT ROWID, BORROWER, AMOUNT FROM IOU";
>       ];
>       rr:subjectMap [
>          rr:column "ROWID";
>          rr:termType rr:BlankNode
>       ];
>       rr:predicateObjectMap [
>          rr:predicate <IOU#BORROWER>;
>          rr:objectMap [ rr:column "BORROWER" ];
>       ];
>       rr:predicateObjectMap [
>          rr:predicate <IOU#AMOUNT>;
>          rr:objectMap [ rr:column "AMOUNT" ];
>       ].
> 
> Now, how to do this without the ROWID vendor extension???
> 
> 
> ----
> 
> For the record. With a lean direct mapping, the desired output graph would be:
> 
>    _:1 <IOU#BORROWER> "Alice".
>    _:1 <IOU#AMOUNT> 10.
>    _:2 <IOU#BORROWER> "Bob".
>    _:2 <IOU#AMOUNT> 5.
>    _:3 <IOU#BORROWER> "Charlie".
>    _:3 <IOU#AMOUNT> 10.
> 
> The query result would be:
> 
>    ?x  | ?property      | ?value
>    ----+----------------+----------
>    _:3 | <IOU#BORROWER> | "Charlie"
>    _:3 | <IOU#AMOUNT>   | 10
>    _:1 |                |
>    _:3 |                |
> 
> The standard-compliant SQL query would be as above, but replace ROWID with something like (BORROWER || '@@@separator@@@' || AMOUNT), and add DISTINCT to each SELECT.
> 
> The R2RML query would be the same as above with the following changes:
> 
>       rr:logicalTable [
>          rr:tableName "IOU";
>       ];
>       rr:subjectMap [
>          rr:template "{BORROWER}@@@separator@@@{AMOUNT}";
>          rr:termType rr:BlankNode;
>       ];
> 
> So, implementing the lean direct mapping is not hard using just standard SQL.
> 
> Best,
> Richard

-- 
-ericP

Received on Wednesday, 2 May 2012 21:40:36 UTC