Reordering of complex SQL queries involving GROUPBYs, joins, outer joins and full outer joins

• US 5,713,015 A
• Filed: 05/30/1996
• Issued: 01/27/1998
• Est. Priority Date: 05/30/1996
• Status: Expired due to Term

• Current Assignee: International Business Machines Corporation
• Original Assignee: International Business Machines Corporation
• Inventors: Iyer, Balakrishna Raghavendra, Goel, Piyush
• Primary Examiner(s): Kulik, Paul V.
• Application Number:
  US08/655,300
• Time in Patent Office: 607 Days
• Field of Search: 395/601, 395/602, 395/603, 395/604
• US Class Current: 1/1
• CPC Class Codes: G06F 16/24537 of operators
• CPC Class Codes: G06F 16/24547 Optimisations to support specific applications; Extensibility of optimisers
• CPC Class Codes: Y10S 707/99932 Access augmentation or optimizing
• CPC Class Codes: Y10S 707/99934 Query formulation, input preparation, or translation

Abstract

A method, apparatus, and article of manufacture for query simplification by applying generalized inference propagation and generalized transitive closure in SQL queries having selection, projection, join, outer join, and intersection operations. The disclosed transformations and enumeration method unify and solve the problems of 1) unnesting join aggregate queries, and 2) complete enumeration of queries containing outer joins, when the outer join predicate references an aggregated value, or the predicate references more than two base relations in a query subtree. The system first eliminates redundant sub-expressions and modifies expensive binary operations to inexpensive binary operations, then converts complex predicates to simple predicates by application of a generalized selection (GS) operator.

Claims

1. A method of simplifying an SQL query in a computer having a memory, the SQL query being performed by the computer to retrieve data from a relational database stored in a electronic storage device coupled to the computer, the method comprising the steps of:

(a) iteratively eliminating, in the memory of the computer, redundant sub-expressions from the SQL query and modifying expensive binary operations in the SQL query to inexpensive binary operations, so that only simple and complex predicates remain in the SQL query; and

(b) iteratively converting, in the memory of the computer, the complex predicates remaining in the SQL query to simple predicates by application of a generalized selection (GS) operator.

2. The method of claim 1 further comprising the step of iteratively applying, in the memory of the computer, a simplification identity to a SELECT DISTINCT operator in the SQL query.

3. The method of claim 1 further comprising the step of iteratively applying, in the memory of the computer, a simplification identity for a push-up of a GROUPBY operator in the SQL query.

4. The method of claim 1 wherein the GS operator, σ

_p^* r₂,r₃ ! (r₁), of relation r₁ with respect to relations r₂ and r₃ comprises the relation <

R₁, V₁, E>

, wherein;

space="preserve" listing-type="equation">E'"'"'=σ

.sub.p (r.sub.1){π

.sub.R.sbsb.2.sup.c.sub.V.sbsb.2 (r.sub.1)-π

.sub.R.sbsb.2.sup.c.sub.V.sbsb.2 (σ

.sub.p (r.sub.1))}{π

.sub.R.sbsb.3.sup.c.sub.V.sbsb.3 (r.sub.1)-π

.sub.R.sbsb.3.sup.c.sub.V.sbsb.3 (σ

.sub.p (r.sub.1))}

and wherein r₁ =<

R₁, V₁,E₁ >

, r₂ =<

R₂,V₂,E₂ >

, and r₃ =<

R₃,V₃,E₃ >

comprise three relations such that R₂ .OR right.R₁, R₃ .OR right.R₁, R₂ ∩

R₃ =φ

, V₂ .OR right.V₁, V₃ .OR right.V₁, and V₂ ∩

V₃ =φ

, and p denotes a null-intolerant predicate in R₁.

5. The method as set forth in claim 1 above, wherein the iteratively converting step comprises the step of applying a simplification expression to the SQL query comprising:

##EQU22## wherein X_i =<

R_i,V_i,E_i >

are relational expressions for 1≦

i≦

3, and p_i,j denote the predicates between expressions X_i and X_j.

6. The method as set forth in claim 1 above, wherein the iteratively converting step comprises the step of applying a simplification expression to the SQL query comprising:

##EQU23## wherein X_i =<

R_i, V_i, E_i >

are relational expressions for 1≦

i≦

3, and p_i,j denote the predicates between expressions X_i and X_j.

7. The method as set forth in claim 1 above, wherein the iteratively converting step comprises the step of applying a simplification expression to the SQL query comprising:

##EQU24## wherein X_i =<

R_i, V_i, E_i >

are relational expressions for 1≦

i≦

3, and p_i,j denote the predicates between expressions X_i and X_j.

8. The method as set forth in claim 1 above, wherein the iteratively converting step comprises the step of applying a simplification expression to the SQL query comprising:

##EQU25## wherein X_i =<

R_i, V_i, E_i >

are relational expressions for 1≦

i≦

3, and p_i,j denote the predicates between expressions X_i and X_j.

9. The method as set forth in claim 1 above, wherein the iteratively converting step comprises the step of applying a simplification expression to the SQL query comprising:

##EQU26## wherein X_i =<

R_i, V_i, E_i >

are relational expressions for 1≦

i≦

3, and p_i,j denote the predicates between expressions X_i and X_j.

10. The method as set forth in claim 1 above, wherein the iteratively converting step comprises the step of applying a simplification expression to the SQL query comprising:

##EQU27## wherein X_i =<

R_i, V_i, E_i >

are relational expressions for 1≦

i≦

3, and p_i,j denote the predicates between expressions X_i and X_j.

11. The method as set forth in claim 1 above, wherein the iteratively converting step comprises the step of applying a simplification expression to the SQL query comprising:

##EQU28## wherein X_i =<

R_i, V_i, V_i >

are relational expressions for 1≦

i≦

3, and p_i,j denote the predicates between expressions X_i and X_j.

12. The method as set forth in claim 1 above, wherein the iteratively converting step comprises the step of applying a simplification expression to the SQL query comprising:

##EQU29## wherein X_i =<

R_i, V_i, E_i >

are relational expressions for 1≦

i≦

3, and p_i,j denote the predicates between expressions X_i and X_j.

13. The method as set forth in claim 1 above, wherein the iteratively converting step comprises the step of applying a simplification expression to the SQL query comprising:

##EQU30## wherein X_i =<

R_i, V_i, E_i >

are relational expressions for 1≦

i≦

3, and p_i,j denote the predicates between expressions X_i and X_j.

14. The method as set forth in claim 1 above, wherein the iteratively converting step comprises the step of applying a simplification expression to the SQL query comprising:

##EQU31## wherein X_i =<

R_i, V_i, E_i >

are relational expressions for 1≦

i≦

3, and p_i,j denote the predicates between expressions X_i and X_j.

15. The method as set forth in claim 1 above, wherein the iteratively converting step comprises the step of applying a simplification expression to the SQL query comprising:

##EQU32## wherein X_i =<

R_i, V_i, E_i >

are relational expressions for 1≦

i≦

3, and p_i,j denote the predicates between expressions X_i and X_j.

16. The method as set forth in claim 1 above, wherein the iteratively converting step comprises the step of applying a simplification expression to the SQL query comprising:

##EQU33## wherein X_i =<

R_i, V_i, E_i >

are relational expressions for 1≦

i≦

3, and p_i,j denote the predicates between expressions X_i and X_j.

17. The method as set forth in claim 1 above, wherein the iteratively converting step comprises the step of applying a simplification expression to the SQL query comprising:

##EQU34## wherein X_i =<

R_i, V_i, E_i >

are relational expressions for 1≦

i≦

3, and p_i,j denote the predicates between expressions X_i and X_j.

18. An apparatus for simplifying an SQL query, comprising:

(a) a computer having a memory and an electronic storage device coupled thereto, the data storage device storing a relational database;

(b) means, performed by the computer, for accepting the SQL query into the memory of the computer, the SQL query being executed by the computer to retrieve data from a relational database stored in the computer;

(c) means, performed by the computer, for iteratively eliminating redundant sub-expressions in the SQL query and modifying expensive binary operations in the SQL query to inexpensive binary operations, so that only simple and complex predicates remain in the SQL query; and

(d) means, performed by the computer, for iteratively converting the complex predicates in the SQL query to simple predicates by application of a generalized selection (GS) operator.

20. The apparatus of claim 18 further comprising means for iteratively applying, in the memory of the computer, a simplification identity to a SELECT DISTINCT operator in the SQL query.

21. The apparatus of claim 18 further comprising means for iteratively applying, in the memory of the computer, a simplification identity for a push-up of a GROUPBY operator in the SQL query.

22. The apparatus of claim 18 wherein the GS operator, σ

_p^* r₂,r₃ !(r₁), of relation r₁ with respect to relations r₂ and r₃ comprises the relation <

R₁, V₁, E'"'"'>

, wherein;

space="preserve" listing-type="equation">E'"'"'=σ

.sub.p (r.sub.1){π

.sub.R.sbsb.2.sup.c.sub.v.sbsb.2 (r.sub.1)-π

.sub.R.sbsb.2.sup.c.sub.v.sbsb.2 (σ

.sub.p (r.sub.1))}{π

.sub.R.sbsb.3.sup.c.sub.v.sbsb.3 (r.sub.1)-π

.sub.R.sbsb.3.sup.c.sub.v.sbsb.3 (σ

.sub.p (r.sub.1))}

and wherein R₁ =<

R₁, V₁, E₁ >

, r₂ =<

R₂, V₂, E₂ >

, and r₃ =<

R₃, V₃, E₃ >

comprise three relations such that R₂ .OR right.R₁, R₃ .OR right.R₁, R₂ ∩

R₃ =φ

, V₂ .OR right.V₁, V₃ .OR right.V₁, and V₂ ∩

V₃ =φ

, and p denotes a null-intolerant predicate in R₁.

23. The apparatus as set forth in claim 18 above, wherein the means for iteratively converting comprises means for applying a simplification expression to the SQL query comprising:

##EQU35## wherein X₁ =<

R_i, V_i, E_i >

are relational expressions for 1≦

i≦

3, and p_i,j denote the predicates between expressions X_i and X_j.

24. The apparatus as set forth in claim 18 above, wherein the means for iteratively converting comprises means for applying a simplification expression to the SQL query comprising:

##EQU36## wherein X_i =<

R_i, V_i, E_i >

are relational expressions for 1≦

i≦

3, and p_i,j denote the predicates between expressions X_i and X_j.

25. The apparatus as set forth in claim 18 above, wherein the means for iteratively converting comprises means for applying a simplification expression to the SQL query comprising:

##EQU37## wherein X_i =<

R_i, V_i, E_i >

are relational expressions for 1≦

i≦

3, and p_i,j denote the predicates between expressions X_i and X_j.

26. The apparatus as set forth in claim 18 above, wherein the means for iteratively converting comprises means for applying a simplification expression to the SQL query comprising:

##EQU38## wherein X_i =<

R_i, V_i, E_i >

are relational expressions for 1≦

i≦

3, and p_i,j denote the predicates between expressions X_i and X_j.

27. The apparatus as set forth in claim 18 above, wherein the means for iteratively converting comprises means for applying a simplification expression to the SQL query comprising:

##EQU39## wherein X_i =<

R_i, V_i, E_i >

are relational expressions for 1≦

i≦

3, and p_i,j denote the predicates between expressions X_i and X_j.

28. The apparatus as set forth in claim 18 above, wherein the means for iteratively converting comprises means for applying a simplification expression to the SQL query comprising:

##EQU40## wherein X_i =<

R_i, V_i, E_i >

are relational expressions for 1≦

i≦

3, and p_i,j denote the predicates between expressions X_i and X_j.

29. The apparatus as set forth in claim 18 above, wherein the means for iteratively converting comprises means for applying a simplification expression to the SQL query comprising:

##EQU41## wherein X_i =<

R_i, V_i, E_i >

are relational expressions for 1≦

i≦

3, and p_i,j denote the predicates between expressions X_i and X_j.

30. The apparatus as set forth in claim 18 above, wherein the means for iteratively converting comprises means for applying a simplification expression to the SQL query comprising:

##EQU42## wherein X_i =<

R_i, V_i, E_i >

are relational expressions for 1≦

i≦

3, and p_i,j denote the predicates between expressions X_i and X_j.

31. The apparatus as set forth in claim 18 above, wherein the means for iteratively converting comprises means for applying a simplification expression to the SQL query comprising:

##EQU43## wherein X_i =<

R_i, V_i, E_i >

are relational expressions for 1≦

i≦

3, and p_i,j denote the predicates between expressions X_i and X_j.

32. The apparatus as set forth in claim 18 above, wherein the means for iteratively converting comprises means for applying a simplification expression to the SQL query comprising:

##EQU44## wherein X_i =<

R_i, V_i, E_i >

are relational expressions for 1≦

i≦

3, and p_i,j denote the predicates between expressions X_i and X_j.

33. The apparatus as set forth in claim 18 above, wherein the means for iteratively converting comprises means for applying a simplification expression to the SQL query comprising:

##EQU45## wherein X_i =<

R_i, V_i, E_i >

are relational expressions for 1≦

i≦

3, and p_i,j denote the predicates between expressions X_i and X_j.

34. The apparatus as set forth in claim 18 above, wherein the means for iteratively converting comprises means for applying a simplification expression to the SQL query comprising:

##EQU46## wherein X_i =<

R_i, V_i, E_i >

are relational expressions for 1≦

i≦

3, and p_i,j denote the predicates between expressions X_i and X_j.

35. The apparatus as set forth in claim 18 above, wherein the means for iteratively converting comprises means for applying a simplification expression to the SQL query comprising:

##EQU47## wherein X_i =<

R_i, V_i, E_i >

are relational expressions for 1≦

i≦

3, and p_i,j denote the predicates between expressions X_i and X_j.

19. A program storage device readable by a computer, tangibly embodying a program of instructions executable by the computer to perform method steps for simplifying an SQL query in a computer having a memory, the SQL query being performed by the computer to retrieve data from a relational database stored in an electronic storage device coupled to the computer, the method comprising the steps of:

(a) iteratively eliminating, in the memory of the computer, redundant sub-expressions in the SQL query and modifying expensive binary operations in the SQL query to inexpensive binary operations, so that only simple and complex predicates remain in the SQL query; and

(b) iteratively converting, in the memory of the computer, the complex predicates in the SQL query to simple predicates by application of a generalized selection operator.

36. The method of claim 19 further comprising the step of iteratively applying, in the memory of the computer, a simplification identity to a SELECT DISTINCT operator in the SQL query.

37. The method of claim 19 further comprising the step of iteratively applying, in the memory of the computer, a simplification identity for a push-up of a GROUPBY operator in the SQL query.

38. The method of claim 19 wherein the GS operator, σ

_p^* r₂, r₃ !(r₁), of relation r₁ with respect to relations r₂ and r₃ comprises the relation <

R₁, V₁, E'"'"'>

, wherein;

space="preserve" listing-type="equation">E'"'"'=σ

.sub.p (r.sub.1){π

.sub.R.sbsb.2.sup.c.sub.V.sbsb.2 (r.sub.1)-π

.sub.R.sbsb.2.sup.c.sub.V.sbsb.2 (σ

.sub.p (r.sub.1))}{π

.sub.R.sbsb.3.sup.c.sub.V.sbsb.3 (r.sub.1)-π

.sub.R.sbsb.3.sup.c.sub.V.sbsb.3 (σ

.sub.p (r.sub.1))}

and wherein r₁ =<

R₁, V₁, E₁ >

, r₂ =<

R₂, V₂, E₂ >

, and r₃ =<

R₃, V₃, E₃ >

comprise three relations such that R₂ .OR right.R₁, R₃ .OR right.R₁, R₂ ∩

R₃ =φ

, V₂ .OR right.V₁, V₃ .OR right.V₁, and V₂ ∩

V₃ =φ

, and p denotes a null-intolerant predicate in R₁.

39. The method as set forth in claim 19 above, wherein the iteratively converting step comprises the step of applying a simplification expression to the SQL query comprising:

##EQU48## wherein X_i =<

R_i, V_i, E_i >

are relational expressions for 1≦

i≦

3, and p_i,j denote the predicates between expressions X₁ and X_j.

40. The method as set forth in claim 19 above, wherein the iteratively converting step comprises the step of applying a simplification expression to the SQL query comprising:

##EQU49## wherein X_i =<

R_i, V_i, E_i >

are relational expressions for 1≦

i≦

3, and p_i,j denote the predicates between expressions X_i and X_j.

41. The method as set forth in claim 19 above, wherein the iteratively converting step comprises the step of applying a simplification expression to the SQL query comprising:

##EQU50## wherein X_i =<

R_i, V_i, E_i >

are relational expressions for 1≦

i≦

3, and p_i,j denote the predicates between expressions X_i and X_j.

42. The method as set forth in claim 19 above, wherein the iteratively converting step comprises the step of applying a simplification expression to the SQL query comprising:

##EQU51## wherein X_i =<

R_i, V_i, E_i >

are relational expressions for 1≦

i≦

3, and p_i,j denote the predicates between expressions X_i and X_j.

43. The method as set forth in claim 19 above, wherein the iteratively converting step comprises the step of applying a simplification expression to the SQL query comprising:

##EQU52## wherein X_i =<

R_i, V_i, E_i >

are relational expressions for 1≦

i≦

3, and p_i,j denote the predicates between expressions X_i and X_j.

44. The method as set forth in claim 19 above, wherein the iteratively converting step comprises the step of applying a simplification expression to the SQL, query comprising:

##EQU53## wherein X_i =<

R_i, V_i, E_i >

are relational expressions for 1≦

i≦

3, and p_i,j denote the predicates between expressions X_i and X_j.

45. The method as set forth in claim 19 above, wherein the iteratively converting step comprises the step of applying a simplification expression to the SQL query comprising:

##EQU54## wherein X_i =<

R_i, V_i, E_i >

are relational expressions for 1≦

i≦

3, and p_i,j denote the predicates between expressions X_i and X_j.

46. The method as set forth in claim 19 above, wherein the iteratively converting step comprises the step of applying a simplification expression to the SQL query comprising:

##EQU55## wherein X_i =<

R_i, V_i, E_i >

are relational expressions for 1≦

i≦

3, and p_i,j denote the predicates between expressions X_i and X_j.

47. The method as set forth in claim 19 above, wherein the iteratively converting step comprises the step of applying a simplification expression to the SQL query comprising:

##EQU56## wherein X_i =<

R_i, V_i, E_i >

are relational expressions for 1≦

i≦

3, and p_i,j denote the predicates between expressions X_i and X_j.

48. The method as set forth in claim 19 above, wherein the iteratively converting step comprises the step of applying a simplification expression to the SQL query comprising:

##EQU57## wherein X_i =<

R_i, V_i, E_i >

are relational expressions for 1≦

i≦

3, and p_i,j denote the predicates between expressions X_i and X_j.

49. The method as set forth in claim 19 above, wherein the iteratively converting step comprises the step of applying a simplification expression to the SQL query comprising:

##EQU58## wherein X_i =<

R_i, V_i, E_i >

are relational expressions for 1≦

i≦

3, and p_i,j denote the predicates between expressions X_i and X_j.

50. The method as set forth in claim 19 above, wherein the iteratively converting step comprises the step of applying a simplification expression to the SQL query comprising:

##EQU59## wherein X_i =<

R_i, V_i, E_i >

are relational expressions for 1≦

i≦

3, and p_i,j denote the predicates between expressions X_i and X_j.

51. The method as set forth in claim 19 above, wherein the iteratively converting step comprises the step of applying a simplification expression to the SQL query comprising:

##EQU60## wherein X_i =<

R_i, V_i, E_i >

are relational expressions for 1≦

i≦

3, and p_i,j denote the predicates between expressions X_i and X_j.