US5855019A
Expired / Lapsed
US
⏱️ 0.0 years remaining
Enumerating projections in SQL queries containing outer and full outer joins in the presence of inner joins
Assignee: International Business Machines Corp
•
Filing: 1997-07-31
•
Granted: 1998-12-29
•
Expires: 2017-07-31
Abstract
Abstract The present invention discloses a method and apparatus for the enumeration of projections (i.e., "SELECT DISTINCT" operations) in SQL queries containing outer and full outer joins in the presence of inner joins without encountering any regression in performance. The present invention removes projections from a given user query by moving the projections to the top of an expression tree representation of the query, wherein the projection removal is performed using algebraic identities rather than rule-based transformations. The present invention also discloses several methods of enumerating different plans or schedules for projection operations and binary operations in the given user query. The present invention can significantly reduce the execution time of a query by selecting the optimal schedule for binary operations and projections between the binary operations. However, the present invention ensures that there is no regression in performance by comparing the cost of the query with the cost of enumerated plans or schedules, thereby ensuring that the optimizations or transformations do not introduce performance penalties.
Inventors
- 👤 Gautam Bhargava
- 👤 Piyush Goel
- 👤 Balakrishna Raghavendra Iyer
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-11-04 22:15
CPC Classifications
G; G06; G06F; G06F16/00; G06F16/20; G06F16/24; G06F16/245; G06F16/2453; G06F16/24534; G06F16/24542; Y; Y10; Y10S; Y10S707/00; Y10S707/99931; Y10S707/99932; Y10S707/99939
Claims Analysis
Total Claims: 36
Claim 1
Independent Claim
251 words
A method of simplifying a query in a computer, the query being performed by the computer to retrieve data from a database stored in a electronic storage device coupled to the computer, the method comprising the steps of: (a) accepting the query into the computer; and (b) replacing a first expression in the query with a second expression, wherein the first expression comprises: δ.sub.X.sbsb.1 (e.sub.x)⊙δ.sub.Y.sbsb.1 (e.sub.y) and the second expression comprises: δ.sub.X.sbsb.1.sub.Y.sbsb.1 (e.sub.x ⊙e.sub.y) wherein: e X =(R X , V X , E X ) is a relation, where R X is a non-empty set of real attributes, V X is a non-empty set of virtual attributes, E X , an extension of the relation, also denoted as ext(e X ), is a set of tuples, X 1 .OR right.R X , and X 2 .OR right.X 1 , e Y =(R Y , V Y , E Y ) is a relation, where R Y is a non-empty set of real attributes, V Y is a non-empty set of virtual attributes, E Y , an extension of the relation, also denoted as ext(e Y ), is a set of tuples, Y 1 .OR right.R Y , and Y 2 .OR right.Y 1 , δ X (r) is a distinct projection operation of relation r onto attributes X, and ⊙ε{, ←, →, ←→}, wherein represents a join operation, ←→ represents a full outer join operation, ← represents a left outer join operation, and → represents a right outer join operation.
Claim 2
Independent Claim
251 words
A method of simplifying a query in a computer, the query being performed by the computer to retrieve data from a database stored in a electronic storage device coupled to the computer, the method comprising the steps of: (a) accepting the query into the computer; and (b) replacing a first expression in the query with a second expression, wherein the first expression comprises: δ.sub.X.sbsb.1 (e.sub.x)⊙δ.sub.Y.sbsb.1 (e.sub.y) and the second expression comprises: δ.sub.X.sbsb.1.sub.Y.sbsb.1 (e.sub.x ⊙e.sub.y) wherein: e X =(R X , V X , E X ) is a relation, where R X is a non-empty set of real attributes, V X is a non-empty set of virtual attributes, E X , an extension of the relation, also denoted as ext(e X ), is a set of tuples, X 1 .OR right.R X , and X 2 .OR right.X 1 , e Y =(R Y , V Y , E Y ) is a relation, where R Y is a non-empty set of real attributes, V Y is a non-empty set of virtual attributes, E Y , an extension of the relation, also denoted as ext(e Y ), is a set of tuples, Y 1 .OR right.R Y , and Y 2 .OR right.Y 1 , δ X (r) is a distinct projection operation of relation r onto attributes X, and ⊙ε{, ←, →, ←→}, wherein represents a join operation, ←→ represents a full outer join operation, ← represents a left outer join operation, and → represents a right outer join operation.
Claim 3
Independent Claim
267 words
A method of simplifying a query in a computer, the query being performed by the computer to retrieve data from a database stored in a electronic storage device coupled to the computer, the method comprising the steps of: (a) accepting the query into the computer; and (b) replacing a first expression in the query with a second expression, wherein the first expression comprises: π.sub.X.sbsb.2 δ.sub.X.sbsb.1 (e.sub.x)⊙π.sub.Y.sbsb.2 δ.sub.Y.sbsb.1 (e.sub.y) and the second expression comprises: π.sub.X.sbsb.2.sub.Y.sbsb.2 δ.sub.X.sbsb.1.sub.Y.sbsb.1 (e.sub.X ⊙e.sub.Y) wherein: e X =(R X , V X , E X ) is a relation, where R X is a non-empty set of real attributes, V X is a non-empty set of virtual attributes, E X , an extension of the relation, also denoted as ext(e X ), is a set of tuples, X 1 .OR right.R X , and X 2 .OR right.X 1 , e Y =(R Y , V Y , E Y ) is a relation, where R Y is a non-empty set of real attributes, V Y is a non-empty set of virtual attributes, E Y , an extension of the relation, also denoted as ext(e Y ), is a set of tuples, Y 1 .OR right.R Y , and Y 2 .OR right.Y 1 , π X (r) is a projection operation of relation r onto attributes X, δ X (r) is a distinct projection operation of relation r onto attributes X, and ⊙ε{, ←, →, ←→}, wherein represents a join operation, ←→ represents a full outer join operation, ← represents a left outer join operation, and → represents a right outer join operation.
Claim 4
Independent Claim
267 words
A method of simplifying a query in a computer, the query being performed by the computer to retrieve data from a database stored in a electronic storage device coupled to the computer, the method comprising the steps of: (a) accepting the query into the computer; and (b) replacing a first expression in the query with a second expression, wherein the first expression comprises: π.sub.X.sbsb.2 δ.sub.X.sbsb.1 (e.sub.x)⊙π.sub.Y.sbsb.2 δ.sub.Y.sbsb.1 (e.sub.y) and the second expression comprises: π.sub.X.sbsb.2.sub.Y.sbsb.2 δ.sub.X.sbsb.1.sub.Y.sbsb.1 (e.sub.X ⊙e.sub.Y) wherein: e X =(R X , V X , E X ) is a relation, where R X is a non-empty set of real attributes, V X is a non-empty set of virtual attributes, E X , an extension of the relation, also denoted as ext(e X ), is a set of tuples, X 1 .OR right.R X , and X 2 .OR right.X 1 , e Y =(R Y , V Y , E Y ) is a relation, where R Y is a non-empty set of real attributes, V Y is a non-empty set of virtual attributes, E Y , an extension of the relation, also denoted as ext(e Y ), is a set of tuples, Y 1 .OR right.R Y , and Y 2 .OR right.Y 1 , π X (r) is a projection operation of relation r onto attributes X, δ X (r) is a distinct projection operation of relation r onto attributes X, and ⊙ε{, ←, →, ←→}, wherein represents a join operation, ←→ represents a full outer join operation, ← represents a left outer join operation, and → represents a right outer join operation.
Claim 5
Independent Claim
251 words
A method of simplifying a query in a computer, the query being performed by the computer to retrieve data from a database stored in a electronic storage device coupled to the computer, the method comprising the steps of: (a) accepting the query into the computer; and (b) replacing a first expression in the query with a second expression, wherein the first expression comprises: π.sub.X.sbsb.1 (e.sub.x)⊙δ.sub.Y.sbsb.1 (e.sub.y) and the second expression comprises: π.sub.X.sbsb.1.sub.Y.sbsb.1 δ.sub.V.sbsb.x.sub.X.sbsb.1.sub.Y.sbsb.1 (e.sub.x ⊙e.sub.y) wherein: e X =(R X V X , E X ) is a relation, where R X is a non-empty set of real attributes, V X is a non-empty set of virtual attributes, E X , an extension of the relation, also denoted as ext(e X ), is a set of tuples, and X 1 .OR right.R X , e Y =(R Y , V Y ,E Y ) is a relation, where R Y is a non-empty set of real attributes, V Y is a non-empty set of virtual attributes, E Y , an extension of the relation, also denoted as ext(e Y ), is a set of tuples, and Y 1 .OR right.R Y , π X (r) is a projection operation of relation r onto attributes X, δ X (r) is a distinct projection operation of relation r onto attributes X, and ⊙ε{, ←, →, ←→}, wherein represents a join operation, ←→ represents a full outer join operation, ← represents a left outer join operation, and → represents a right outer join operation.
Claim 6
Independent Claim
251 words
A method of simplifying a query in a computer, the query being performed by the computer to retrieve data from a database stored in a electronic storage device coupled to the computer, the method comprising the steps of: (a) accepting the query into the computer; and (b) replacing a first expression in the query with a second expression, wherein the first expression comprises: π.sub.X.sbsb.1 (e.sub.x)⊙δ.sub.Y.sbsb.1 (e.sub.y) and the second expression comprises: π.sub.X.sbsb.1.sub.Y.sbsb.1 δ.sub.V.sbsb.x.sub.X.sbsb.1.sub.Y.sbsb.1 (e.sub.x ⊙e.sub.y) wherein: e X =(R X V X , E X ) is a relation, where R X is a non-empty set of real attributes, V X is a non-empty set of virtual attributes, E X , an extension of the relation, also denoted as ext(e X ), is a set of tuples, and X 1 .OR right.R X , e Y =(R Y , V Y ,E Y ) is a relation, where R Y is a non-empty set of real attributes, V Y is a non-empty set of virtual attributes, E Y , an extension of the relation, also denoted as ext(e Y ), is a set of tuples, and Y 1 .OR right.R Y , π X (r) is a projection operation of relation r onto attributes X, δ X (r) is a distinct projection operation of relation r onto attributes X, and ⊙ε{, ←, →, ←→}, wherein represents a join operation, ←→ represents a full outer join operation, ← represents a left outer join operation, and → represents a right outer join operation.
Claim 7
Independent Claim
260 words
A method of simplifying a query in a computer, the query being performed by the computer to retrieve data from a database stored in a electronic storage device coupled to the computer, the method comprising the steps of: (a) accepting the query into the computer; and (b) replacing a first expression in the query with a second expression, wherein the first expression comprises: π.sub.X.sbsb.2 δ.sub.X.sbsb.1 (e.sub.x)⊙π.sub.Y.sbsb.1 (e.sub.y) and the second expression comprises: π.sub.X.sbsb.2.sub.Y.sbsb.1 δ.sub.V.sbsb.y.sub.X.sbsb.1.sub.Y.sbsb.1 (e.sub.X ⊙e.sub.Y) wherein: e X =(R X , V X , E X ) is a relation, where R X is a non-empty set of real attributes, V X is a non-empty set of virtual attributes, E X , an extension of the relation, also denoted as ext(e X ), is a set of tuples, X 1 .OR right.R X , and X 2 .OR right.X 1 , e Y =(R Y , V Y , E Y ) is a relation, where R Y is a non-empty set of real attributes, V Y is a non-empty set of virtual attributes, E Y , an extension of the relation, also denoted as ext(e Y ), is a set of tuples, and Y 1 .OR right.R Y , π X (r) is a projection operation of relation r onto attributes X, δ X (r) is a distinct projection operation of relation r onto attributes X, and ⊙ε{, ←, →, ←→}, wherein represents a join operation, ←→ represents a full outer join operation, ← represents a left outer join operation, and → represents a right outer join operation.
Claim 8
Independent Claim
260 words
A method of simplifying a query in a computer, the query being performed by the computer to retrieve data from a database stored in a electronic storage device coupled to the computer, the method comprising the steps of: (a) accepting the query into the computer; and (b) replacing a first expression in the query with a second expression, wherein the first expression comprises: π.sub.X.sbsb.2 δ.sub.X.sbsb.1 (e.sub.x)⊙π.sub.Y.sbsb.1 (e.sub.y) and the second expression comprises: π.sub.X.sbsb.2.sub.Y.sbsb.1 δ.sub.V.sbsb.y.sub.X.sbsb.1.sub.Y.sbsb.1 (e.sub.X ⊙e.sub.Y) wherein: e X =(R X , V X , E X ) is a relation, where R X is a non-empty set of real attributes, V X is a non-empty set of virtual attributes, E X , an extension of the relation, also denoted as ext(e X ), is a set of tuples, X 1 .OR right.R X , and X 2 .OR right.X 1 , e Y =(R Y , V Y , E Y ) is a relation, where R Y is a non-empty set of real attributes, V Y is a non-empty set of virtual attributes, E Y , an extension of the relation, also denoted as ext(e Y ), is a set of tuples, and Y 1 .OR right.R Y , π X (r) is a projection operation of relation r onto attributes X, δ X (r) is a distinct projection operation of relation r onto attributes X, and ⊙ε{, ←, →, ←→}, wherein represents a join operation, ←→ represents a full outer join operation, ← represents a left outer join operation, and → represents a right outer join operation.
Claim 9
Independent Claim
260 words
A method of simplifying a query in a computer, the query being performed by the computer to retrieve data from a database stored in a electronic storage device coupled to the computer, the method comprising the steps of: (a) accepting the query into the computer; and (b) replacing a first expression in the query with a second expression, wherein the first expression comprises: π.sub.X.sbsb.2 δ.sub.X.sbsb.1 (e.sub.x)⊙δ.sub.Y.sbsb.1 (e.sub.y) and the second expression comprises: π.sub.X.sbsb.2.sub.Y.sbsb.1 δ.sub.X.sbsb.1.sub.Y.sbsb.1 (e.sub.x ⊙e.sub.Y) wherein: e X =(R X , V X , E X ) is a relation, where R X is a non-empty set of real attributes, V X is a non-empty set of virtual attributes, E X , an extension of the relation, also denoted as ext(e X ), is a set of tuples, X 1 .OR right.R X , and X 2 .OR right.X 1 , e Y =(R Y , V Y , E Y ) is a relation, where R Y is a non-empty set of real attributes, V Y is a non-empty set of virtual attributes, E Y , an extension of the relation, also denoted as ext(e Y ), is a set of tuples, and Y 1 .OR right.R Y , π X (r) is a projection operation of relation r onto attributes X, δ X (r) is a distinct projection operation of relation r onto attributes X, and ⊙ε{, ←, →, ←→}, wherein represents a join operation, ←→ represents a full outer join operation, ← represents a left outer join operation, and → represents a right outer join operation.
Claim 10
Independent Claim
260 words
A method of simplifying a query in a computer, the query being performed by the computer to retrieve data from a database stored in a electronic storage device coupled to the computer, the method comprising the steps of: (a) accepting the query into the computer; and (b) replacing a first expression in the query with a second expression, wherein the first expression comprises: π.sub.X.sbsb.2 δ.sub.X.sbsb.1 (e.sub.x)⊙δ.sub.Y.sbsb.1 (e.sub.y) and the second expression comprises: π.sub.X.sbsb.2.sub.Y.sbsb.1 δ.sub.X.sbsb.1.sub.Y.sbsb.1 (e.sub.x ⊙e.sub.Y) wherein: e X =(R X , V X , E X ) is a relation, where R X is a non-empty set of real attributes, V X is a non-empty set of virtual attributes, E X , an extension of the relation, also denoted as ext(e X ), is a set of tuples, X 1 .OR right.R X , and X 2 .OR right.X 1 , e Y =(R Y , V Y , E Y ) is a relation, where R Y is a non-empty set of real attributes, V Y is a non-empty set of virtual attributes, E Y , an extension of the relation, also denoted as ext(e Y ), is a set of tuples, and Y 1 .OR right.R Y , π X (r) is a projection operation of relation r onto attributes X, δ X (r) is a distinct projection operation of relation r onto attributes X, and ⊙ε{, ←, →, ←→}, wherein represents a join operation, ←→ represents a full outer join operation, ← represents a left outer join operation, and → represents a right outer join operation.
Claim 11
Independent Claim
255 words
A method of simplifying a query in a computer, the query being performed by the computer to retrieve data from a database stored in a electronic storage device coupled to the computer, the method comprising the steps of: (a) accepting the query into the computer; and (b) applying an identity to the query, wherein the identity comprises: ##EQU5## and wherein: e X =(R X , V X , E X ) is a relation, where R X is a non-empty set of real attributes, V X is a non-empty set of virtual attributes, E X , an extension of the relation, also denoted as ext(e X ), is a set of tuples, and X 1 .OR right.R X , e Y =(R Y , V Y , E Y ) is a relation, where R Y is a non-empty set of real attributes, V Y is a non-empty set of virtual attributes, E Y , an extension of the relation, also denoted as ext(e Y ), is a set of tuples, and Y 1 .OR right.R Y , p xy is a predicate, sch(p xy ) is a schema of p xy , (sch(p xy )∩R X ).OR right.X 1 , (sch(p xy )∩R Y ).OR right.Y 1 , δ X (r) is a distinct projection operation of relation r onto attributes X, and ⊙ε{, ←, →, ←→}, wherein represents a join operation, ←→ represents a full outer join operation, ← represents a left outer join operation, and → represents a right outer join operation.
Claim 12
Independent Claim
255 words
A method of simplifying a query in a computer, the query being performed by the computer to retrieve data from a database stored in a electronic storage device coupled to the computer, the method comprising the steps of: (a) accepting the query into the computer; and (b) applying an identity to the query, wherein the identity comprises: ##EQU5## and wherein: e X =(R X , V X , E X ) is a relation, where R X is a non-empty set of real attributes, V X is a non-empty set of virtual attributes, E X , an extension of the relation, also denoted as ext(e X ), is a set of tuples, and X 1 .OR right.R X , e Y =(R Y , V Y , E Y ) is a relation, where R Y is a non-empty set of real attributes, V Y is a non-empty set of virtual attributes, E Y , an extension of the relation, also denoted as ext(e Y ), is a set of tuples, and Y 1 .OR right.R Y , p xy is a predicate, sch(p xy ) is a schema of p xy , (sch(p xy )∩R X ).OR right.X 1 , (sch(p xy )∩R Y ).OR right.Y 1 , δ X (r) is a distinct projection operation of relation r onto attributes X, and ⊙ε{, ←, →, ←→}, wherein represents a join operation, ←→ represents a full outer join operation, ← represents a left outer join operation, and → represents a right outer join operation.
Claim 13
Independent Claim
255 words
An apparatus for simplifying a query in a computer, the query being performed by the computer to retrieve data from a database stored in a electronic storage device coupled to the computer, the apparatus comprising: (a) a computer; (b) means for accepting the query into the computer; and (c) means for replacing a first expression in the query with a second expression, wherein the first expression comprises: δ.sub.X.sbsb.1 (e.sub.x)⊙δ.sub.Y.sbsb.1 (e.sub.y) and the second expression comprises: δ.sub.X.sbsb.1.sub.Y.sbsb.1 (e.sub.x ⊙e.sub.y) wherein: e X =(R X , V X , E X ) is a relation, where R X is a non-empty set of real attributes, V X is a non-empty set of virtual attributes, E X , an extension of the relation, also denoted as ext(e X ), is a set of tuples, X 1 .OR right.R X , and X 2 .OR right.X 1 , e Y =(R Y , V Y , E Y ) is a relation, where R Y is a non-empty set of real attributes, V Y is a non-empty set of virtual attributes, E Y , an extension of the relation, also denoted as ext(e Y ), is a set of tuples, Y 1 .OR right.R Y , and Y 2 .OR right.Y 1 , δ X (r) is a distinct projection operation of relation r onto attributes X, and ⊙ε{, ←, →, ←→}, wherein represents a join operation, ←→ represents a full outer join operation, ← represents a left outer join operation, and → represents a right outer join operation.
Claim 14
Independent Claim
255 words
An apparatus for simplifying a query in a computer, the query being performed by the computer to retrieve data from a database stored in a electronic storage device coupled to the computer, the apparatus comprising: (a) a computer; (b) means for accepting the query into the computer; and (c) means for replacing a first expression in the query with a second expression, wherein the first expression comprises: δ.sub.X.sbsb.1 (e.sub.x)⊙δ.sub.Y.sbsb.1 (e.sub.y) and the second expression comprises: δ.sub.X.sbsb.1.sub.Y.sbsb.1 (e.sub.x ⊙e.sub.y) wherein: e X =(R X , V X , E X ) is a relation, where R X is a non-empty set of real attributes, V X is a non-empty set of virtual attributes, E X , an extension of the relation, also denoted as ext(e X ), is a set of tuples, X 1 .OR right.R X , and X 2 .OR right.X 1 , e Y =(R Y , V Y , E Y ) is a relation, where R Y is a non-empty set of real attributes, V Y is a non-empty set of virtual attributes, E Y , an extension of the relation, also denoted as ext(e Y ), is a set of tuples, Y 1 .OR right.R Y , and Y 2 .OR right.Y 1 , δ X (r) is a distinct projection operation of relation r onto attributes X, and ⊙ε{, ←, →, ←→}, wherein represents a join operation, ←→ represents a full outer join operation, ← represents a left outer join operation, and → represents a right outer join operation.
Claim 15
Independent Claim
261 words
An apparatus for simplifying a query in a computer, the query being performed by the computer to retrieve data from a database stored in a electronic storage device coupled to the computer, the apparatus comprising: (a) a computer; (b) means for accepting the query into the computer; and (c) means for replacing a first expression in the query with a second expression, wherein the first expression comprises: π.sub.X.sbsb.2 δ.sub.X.sbsb.1 (e.sub.x)⊙π.sub.Y.sbsb.2 δ.sub.Y.sbsb.1 (e.sub.y) and the second expression comprises: π.sub.X.sbsb.2.sub.Y.sbsb.2 δ.sub.X.sbsb.1.sub.Y.sbsb.1 (e.sub.x ⊙e.sub.Y) wherein: e X =(R X , V X , E X ) is a relation, where R X is a non-empty set of real attributes, V X is a non-empty set of virtual attributes, E X , an extension of the relation, also denoted as ext(e X ), is a set of tuples, X 1 .OR right.R X , and X 2 .OR right.X 1 , e Y =(R Y , V Y , E Y ) is a relation, where R Y is a non-empty set of real attributes, V Y is a non-empty set of virtual attributes, E Y , an extension of the relation, also denoted as ext(e Y ), is a set of tuples, Y 1 .OR right.R Y , and Y 2 .OR right.Y 1 , π X (r) is a projection operation of relation r onto attributes X, δ X (r) is a distinct projection operation of relation r onto attributes X, and represents a full outer join operation, ← represents a left outer join operation, and → represents a right outer join operation.
Claim 16
Independent Claim
261 words
An apparatus for simplifying a query in a computer, the query being performed by the computer to retrieve data from a database stored in a electronic storage device coupled to the computer, the apparatus comprising: (a) a computer; (b) means for accepting the query into the computer; and (c) means for replacing a first expression in the query with a second expression, wherein the first expression comprises: π.sub.X.sbsb.2 δ.sub.X.sbsb.1 (e.sub.x)⊙π.sub.Y.sbsb.2 δ.sub.Y.sbsb.1 (e.sub.y) and the second expression comprises: π.sub.X.sbsb.2.sub.Y.sbsb.2 δ.sub.X.sbsb.1.sub.Y.sbsb.1 (e.sub.x ⊙e.sub.Y) wherein: e X =(R X , V X , E X ) is a relation, where R X is a non-empty set of real attributes, V X is a non-empty set of virtual attributes, E X , an extension of the relation, also denoted as ext(e X ), is a set of tuples, X 1 .OR right.R X , and X 2 .OR right.X 1 , e Y =(R Y , V Y , E Y ) is a relation, where R Y is a non-empty set of real attributes, V Y is a non-empty set of virtual attributes, E Y , an extension of the relation, also denoted as ext(e Y ), is a set of tuples, Y 1 .OR right.R Y , and Y 2 .OR right.Y 1 , π X (r) is a projection operation of relation r onto attributes X, δ X (r) is a distinct projection operation of relation r onto attributes X, and represents a full outer join operation, ← represents a left outer join operation, and → represents a right outer join operation.
Claim 17
Independent Claim
257 words
An apparatus for simplifying a query in a computer, the query being performed by the computer to retrieve data from a database stored in a electronic storage device coupled to the computer, the apparatus comprising: (a) a computer; (b) means for accepting the query into the computer; and (c) means for replacing a first expression in the query with a second expression, wherein the first expression comprises: π.sub.X.sbsb.1 (e.sub.x)⊙δ.sub.Y.sbsb.1 (e.sub.y) and the second expression comprises: π.sub.X.sbsb.1.sub.Y.sbsb.1 δ.sub.V.sbsb.x.sub.X.sbsb.1.sub.Y.sbsb.1 (e.sub.x ⊙e.sub.y) wherein: e X =(R X , V X , E X ) is a relation, where R X is a non-empty set of real attributes, V X is a non-empty set of virtual attributes, E X , an extension of the relation, also denoted as ext(e X ), is a set of tuples, and X 1 .OR right.R X , e Y =(R Y , V Y , E Y ) is a relation, where R Y is a non-empty set of real attributes, V Y is a non-empty set of virtual attributes, E Y , an extension of the relation, also denoted as ext(e Y ), is a set of tuples, and Y 1 .OR right.R Y , π X (r) is a projection operation of relation r onto attributes X, δ X (r) is a distinct projection operation of relation r onto attributes X, and ⊙ε{, ←, →, ←→}, wherein represents a join operation, ←→ represents a full outer join operation, ← represents a left outer join operation, and → represents a right outer join operation.
Claim 18
Independent Claim
257 words
An apparatus for simplifying a query in a computer, the query being performed by the computer to retrieve data from a database stored in a electronic storage device coupled to the computer, the apparatus comprising: (a) a computer; (b) means for accepting the query into the computer; and (c) means for replacing a first expression in the query with a second expression, wherein the first expression comprises: π.sub.X.sbsb.1 (e.sub.x)⊙δ.sub.Y.sbsb.1 (e.sub.y) and the second expression comprises: π.sub.X.sbsb.1.sub.Y.sbsb.1 δ.sub.V.sbsb.x.sub.X.sbsb.1.sub.Y.sbsb.1 (e.sub.x ⊙e.sub.y) wherein: e X =(R X , V X , E X ) is a relation, where R X is a non-empty set of real attributes, V X is a non-empty set of virtual attributes, E X , an extension of the relation, also denoted as ext(e X ), is a set of tuples, and X 1 .OR right.R X , e Y =(R Y , V Y , E Y ) is a relation, where R Y is a non-empty set of real attributes, V Y is a non-empty set of virtual attributes, E Y , an extension of the relation, also denoted as ext(e Y ), is a set of tuples, and Y 1 .OR right.R Y , π X (r) is a projection operation of relation r onto attributes X, δ X (r) is a distinct projection operation of relation r onto attributes X, and ⊙ε{, ←, →, ←→}, wherein represents a join operation, ←→ represents a full outer join operation, ← represents a left outer join operation, and → represents a right outer join operation.
Claim 19
Independent Claim
265 words
An apparatus for simplifying a query in a computer, the query being performed by the computer to retrieve data from a database stored in a electronic storage device coupled to the computer, the apparatus comprising: (a) a computer; (b) means for accepting the query into the computer; and (c) means for replacing a first expression in the query with a second expression, wherein the first expression comprises: π.sub.X.sbsb.2 δ.sub.X.sbsb.1 (e.sub.x)⊙π.sub.Y.sbsb.1 (e.sub.y) and the second expression comprises: π.sub.X.sbsb.2.sub.Y.sbsb.1 δ.sub.V.sbsb.y.sub.X.sbsb.1.sub.Y.sbsb.1 (e.sub.x ⊙e.sub.Y) wherein: e X =(R X , V X , E X ) is a relation, where R X is a non-empty set of real attributes, V X is a non-empty set of virtual attributes, E X , an extension of the relation, also denoted as ext(e X ), is a set of tuples, and X 1 .OR right.R X , and X 2 .OR right.X 1 , e Y =(R Y , V Y , E Y ) is a relation, where R Y is a non-empty set of real attributes, V Y is a non-empty set of virtual attributes, E Y , an extension of the relation, also denoted as ext(e Y ), is a set of tuples, and Y 1 .OR right.R Y , π X (r) is a projection operation of relation r onto attributes X, δ X (r) is a distinct projection operation of relation r onto attributes X, and ⊙ε{, ←, →, ←→}, wherein represents a join operation, ←→ represents a full outer join operation, ← represents a left outer join operation, and → represents a right outer join operation.
Claim 20
Independent Claim
265 words
An apparatus for simplifying a query in a computer, the query being performed by the computer to retrieve data from a database stored in a electronic storage device coupled to the computer, the apparatus comprising: (a) a computer; (b) means for accepting the query into the computer; and (c) means for replacing a first expression in the query with a second expression, wherein the first expression comprises: π.sub.X.sbsb.2 δ.sub.X.sbsb.1 (e.sub.x)⊙π.sub.Y.sbsb.1 (e.sub.y) and the second expression comprises: π.sub.X.sbsb.2.sub.Y.sbsb.1 δ.sub.V.sbsb.y.sub.X.sbsb.1.sub.Y.sbsb.1 (e.sub.x ⊙e.sub.Y) wherein: e X =(R X , V X , E X ) is a relation, where R X is a non-empty set of real attributes, V X is a non-empty set of virtual attributes, E X , an extension of the relation, also denoted as ext(e X ), is a set of tuples, and X 1 .OR right.R X , and X 2 .OR right.X 1 , e Y =(R Y , V Y , E Y ) is a relation, where R Y is a non-empty set of real attributes, V Y is a non-empty set of virtual attributes, E Y , an extension of the relation, also denoted as ext(e Y ), is a set of tuples, and Y 1 .OR right.R Y , π X (r) is a projection operation of relation r onto attributes X, δ X (r) is a distinct projection operation of relation r onto attributes X, and ⊙ε{, ←, →, ←→}, wherein represents a join operation, ←→ represents a full outer join operation, ← represents a left outer join operation, and → represents a right outer join operation.
Claim 21
Independent Claim
265 words
An apparatus for simplifying a query in a computer, the query being performed by the computer to retrieve data from a database stored in a electronic storage device coupled to the computer, the apparatus comprising: (a) a computer; (b) means for accepting the query into the computer; and (c) means for replacing a first expression in the query with a second expression, wherein the first expression comprises: π.sub.X.sbsb.2 δ.sub.X.sbsb.1 (e.sub.x)⊙δ.sub.Y.sbsb.1 (e.sub.y) and the second expression comprises: π.sub.X.sbsb.2.sub.Y.sbsb.1 δ.sub.X.sbsb.1.sub.Y.sbsb.1 (e.sub.x ⊙e.sub.Y) wherein: e X =(R X , V X , E X ) is a relation, where R X is a non-empty set of real attributes, V X is a non-empty set of virtual attributes, E X , an extension of the relation, also denoted as ext(e X ), is a set of tuples, and X 1 .OR right.R X , and X 2 .OR right.X 1 , e Y =(R Y , V Y , E Y ) is a relation, where R Y is a non-empty set of real attributes, V Y is a non-empty set of virtual attributes, E Y , an extension of the relation, also denoted as ext(e Y ), is a set of tuples, and Y 1 .OR right.R Y , π X (r) is a projection operation of relation r onto attributes X, δ X (r) is a distinct projection operation of relation r onto attributes X, and ⊙ε{, ←, →, ←→}, wherein represents a join operation, ←→ represents a full outer join operation, ← represents a left outer join operation, and → represents a right outer join operation.
Claim 22
Independent Claim
265 words
An apparatus for simplifying a query in a computer, the query being performed by the computer to retrieve data from a database stored in a electronic storage device coupled to the computer, the apparatus comprising: (a) a computer; (b) means for accepting the query into the computer; and (c) means for replacing a first expression in the query with a second expression, wherein the first expression comprises: π.sub.X.sbsb.2 δ.sub.X.sbsb.1 (e.sub.x)⊙δ.sub.Y.sbsb.1 (e.sub.y) and the second expression comprises: π.sub.X.sbsb.2.sub.Y.sbsb.1 δ.sub.X.sbsb.1.sub.Y.sbsb.1 (e.sub.x ⊙e.sub.Y) wherein: e X =(R X , V X , E X ) is a relation, where R X is a non-empty set of real attributes, V X is a non-empty set of virtual attributes, E X , an extension of the relation, also denoted as ext(e X ), is a set of tuples, and X 1 .OR right.R X , and X 2 .OR right.X 1 , e Y =(R Y , V Y , E Y ) is a relation, where R Y is a non-empty set of real attributes, V Y is a non-empty set of virtual attributes, E Y , an extension of the relation, also denoted as ext(e Y ), is a set of tuples, and Y 1 .OR right.R Y , π X (r) is a projection operation of relation r onto attributes X, δ X (r) is a distinct projection operation of relation r onto attributes X, and ⊙ε{, ←, →, ←→}, wherein represents a join operation, ←→ represents a full outer join operation, ← represents a left outer join operation, and → represents a right outer join operation.
Claim 23
Independent Claim
265 words
An apparatus for simplifying a query in a computer, the query being performed by the computer to retrieve data from a database stored in a electronic storage device coupled to the computer, the apparatus comprising: (a) a computer; (b) means for accepting the query into the computer; and (c) means for applying an identity to the query, wherein the identity comprises: δ.sub.X.sbsb.1.sub.Y.sbsb.1 (e.sub.x ⊙.sup.p.sbsp.xy e.sub.y)=δ.sub.X.sbsb.1 (e.sub.x).sub.⊙.sup.p.sbsp.xy δ.sub.Y.sbsb.1 (e.sub.y) and wherein: e X =(R X , V X , E X ) is a relation, where R X is a non-empty set of real attributes, V X is a non-empty set of virtual attributes, E X , an extension of the relation, also denoted as ext(e X ), is a set of tuples, and X 1 .OR right.R X , e Y =(R Y , V Y , E Y ) is a relation, where R Y is a non-empty set of real attributes, V Y is a non-empty set of virtual attributes, E Y , an extension of the relation, also denoted as ext(e Y ), is a set of tuples, and Y 1 .OR right.R Y , p xy is a predicate, sch(p xy ) is a schema of p xy , (sch(p xy )∩R X ).OR right.X 1 , (sch(p xy )∩R Y ).OR right.Y 1 , δ X (r) is a distinct projection operation of relation r onto attributes X, and ⊙ε{, ←, →, ←→}, wherein represents a join operation, ←→ represents a full outer join operation, ← represents a left outer join operation, and → represents a right outer join operation.
Claim 24
Independent Claim
265 words
An apparatus for simplifying a query in a computer, the query being performed by the computer to retrieve data from a database stored in a electronic storage device coupled to the computer, the apparatus comprising: (a) a computer; (b) means for accepting the query into the computer; and (c) means for applying an identity to the query, wherein the identity comprises: δ.sub.X.sbsb.1.sub.Y.sbsb.1 (e.sub.x ⊙.sup.p.sbsp.xy e.sub.y)=δ.sub.X.sbsb.1 (e.sub.x).sub.⊙.sup.p.sbsp.xy δ.sub.Y.sbsb.1 (e.sub.y) and wherein: e X =(R X , V X , E X ) is a relation, where R X is a non-empty set of real attributes, V X is a non-empty set of virtual attributes, E X , an extension of the relation, also denoted as ext(e X ), is a set of tuples, and X 1 .OR right.R X , e Y =(R Y , V Y , E Y ) is a relation, where R Y is a non-empty set of real attributes, V Y is a non-empty set of virtual attributes, E Y , an extension of the relation, also denoted as ext(e Y ), is a set of tuples, and Y 1 .OR right.R Y , p xy is a predicate, sch(p xy ) is a schema of p xy , (sch(p xy )∩R X ).OR right.X 1 , (sch(p xy )∩R Y ).OR right.Y 1 , δ X (r) is a distinct projection operation of relation r onto attributes X, and ⊙ε{, ←, →, ←→}, wherein represents a join operation, ←→ represents a full outer join operation, ← represents a left outer join operation, and → represents a right outer join operation.
Claim 25
Dependent Claim
268 words
An article of manufacture comprising a computer program carrier embodying one or more instructions of a method of simplifying a query in a computer, the query being performed by the computer to retrieve data from a database stored in a electronic storage device coupled to the computer, the method comprising the steps of: (a) accepting the query into the computer; and (b) replacing a first expression in the query with a second expression, wherein the first expression comprises: δ.sub.X.sbsb.1 (e.sub.x)⊙δ.sub.Y.sbsb.1 (e.sub.y) and the second expression comprises: δ.sub.X.sbsb.1.sub.Y.sbsb.1 (e.sub.x ⊙e.sub.y) wherein: e X =(R X , V X , E X ) is a relation, where R X is a non-empty set of real attributes, V X is a non-empty set of virtual attributes, E X , an extension of the relation, also denoted as ext(e X ), is a set of tuples, and X 1 .OR right.R X , and X 2 .OR right.X 1 , e Y =(R Y , V Y , E Y ) is a relation, where R Y is a non-empty set of real attributes, V Y is a non-empty set of virtual attributes, E Y , an extension of the relation, also denoted as ext(e Y ), is a set of tuples, and Y 1 .OR right.R Y , and Y 2 .OR right.Y 1 , δ X (r) is a distinct projection operation of relation r onto attributes X, and ⊙ε{, ←, →, ←→}, wherein represents a join operation, ←→ represents a full outer join operation, ← represents a left outer join operation, and → represents a right outer join operation.
Claim 26
Dependent Claim
268 words
An article of manufacture comprising a computer program carrier embodying one or more instructions of a method of simplifying a query in a computer, the query being performed by the computer to retrieve data from a database stored in a electronic storage device coupled to the computer, the method comprising the steps of: (a) accepting the query into the computer; and (b) replacing a first expression in the query with a second expression, wherein the first expression comprises: δ.sub.X.sbsb.1 (e.sub.x)⊙δ.sub.Y.sbsb.1 (e.sub.y) and the second expression comprises: δ.sub.X.sbsb.1.sub.Y.sbsb.1 (e.sub.x ⊙e.sub.y) wherein: e X =(R X , V X , E X ) is a relation, where R X is a non-empty set of real attributes, V X is a non-empty set of virtual attributes, E X , an extension of the relation, also denoted as ext(e X ), is a set of tuples, and X 1 .OR right.R X , and X 2 .OR right.X 1 , e Y =(R Y , V Y , E Y ) is a relation, where R Y is a non-empty set of real attributes, V Y is a non-empty set of virtual attributes, E Y , an extension of the relation, also denoted as ext(e Y ), is a set of tuples, and Y 1 .OR right.R Y , and Y 2 .OR right.Y 1 , δ X (r) is a distinct projection operation of relation r onto attributes X, and ⊙ε{, ←, →, ←→}, wherein represents a join operation, ←→ represents a full outer join operation, ← represents a left outer join operation, and → represents a right outer join operation.
Claim 27
Dependent Claim
284 words
An article of manufacture comprising a computer program carrier embodying one or more instructions of a method of simplifying a query in a computer, the query being performed by the computer to retrieve data from a database stored in a electronic storage device coupled to the computer, the method comprising the steps of: (a) accepting the query into the computer; and (b) replacing a first expression in the query with a second expression, wherein the first expression comprises: π.sub.X.sbsb.2 δ.sub.X.sbsb.1 (e.sub.x)⊙π.sub.Y.sbsb.2 δ.sub.Y.sbsb.1 (e.sub.y) and the second expression comprises: π.sub.X.sbsb.2.sub.Y.sbsb.2 δ.sub.X.sbsb.1.sub.Y.sbsb.1 (e.sub.x ⊙e.sub.Y) wherein: e X =(R X , V X , E X ) is a relation, where R X is a non-empty set of real attributes, V X is a non-empty set of virtual attributes, E X , an extension of the relation, also denoted as ext(e X ), is a set of tuples, and X 1 .OR right.R X , and X 2 .OR right.X 1 , e Y =(R Y , V Y , E Y ) is a relation, where R Y is a non-empty set of real attributes, V Y is a non-empty set of virtual attributes, E Y , an extension of the relation, also denoted as ext(e Y ), is a set of tuples, and Y 1 .OR right.R Y , and Y 2 .OR right.Y 1 , π X (r) is a projection operation of relation r onto attributes X, δ X (r) is a distinct projection operation of relation r onto attributes X, and ⊙ε{, ←, →, ←→}, wherein represents a join operation, ←→ represents a full outer join operation, ← represents a left outer join operation, and → represents a right outer join operation.
Claim 28
Dependent Claim
284 words
An article of manufacture comprising a computer program carrier embodying one or more instructions of a method of simplifying a query in a computer, the query being performed by the computer to retrieve data from a database stored in a electronic storage device coupled to the computer, the method comprising the steps of: (a) accepting the query into the computer; and (b) replacing a first expression in the query with a second expression, wherein the first expression comprises: π.sub.X.sbsb.2 δ.sub.X.sbsb.1 (e.sub.x)⊙π.sub.Y.sbsb.2 δ.sub.Y.sbsb.1 (e.sub.y) and the second expression comprises: π.sub.X.sbsb.2.sub.Y.sbsb.2 δ.sub.X.sbsb.1.sub.Y.sbsb.1 (e.sub.x ⊙e.sub.Y) wherein: e X =(R X , V X , E X ) is a relation, where R X is a non-empty set of real attributes, V X is a non-empty set of virtual attributes, E X , an extension of the relation, also denoted as ext(e X ), is a set of tuples, and X 1 .OR right.R X , and X 2 .OR right.X 1 , e Y =(R Y , V Y , E Y ) is a relation, where R Y is a non-empty set of real attributes, V Y is a non-empty set of virtual attributes, E Y , an extension of the relation, also denoted as ext(e Y ), is a set of tuples, and Y 1 .OR right.R Y , and Y 2 .OR right.Y 1 , π X (r) is a projection operation of relation r onto attributes X, δ X (r) is a distinct projection operation of relation r onto attributes X, and ⊙ε{, ←, →, ←→}, wherein represents a join operation, ←→ represents a full outer join operation, ← represents a left outer join operation, and → represents a right outer join operation.
Claim 29
Dependent Claim
268 words
An article of manufacture comprising a computer program carrier embodying one or more instructions of a method of simplifying a query in a computer, the query being performed by the computer to retrieve data from a database stored in a electronic storage device coupled to the computer, the method comprising the steps of: (a) accepting the query into the computer; and (b) replacing a first expression in the query with a second expression, wherein the first expression comprises: π.sub.X.sbsb.1 (e.sub.x)⊙δ.sub.Y.sbsb.1 (e.sub.y) and the second expression comprises: π.sub.X.sbsb.1.sub.Y.sbsb.1 δ.sub.V.sbsb.x.sub.X.sbsb.1.sub.Y.sbsb.1 (e.sub.x ⊙e.sub.y) wherein: e X =(R X , V X , E X ) is a relation, where R X is a non-empty set of real attributes, V X is a non-empty set of virtual attributes, E X , an extension of the relation, also denoted as ext(e X ), is a set of tuples, and X 1 .OR right.R X , e Y =(R Y , V Y , E Y ) is a relation, where R Y is a non-empty set of real attributes, V Y is a non-empty set of virtual attributes, E Y , an extension of the relation, also denoted as ext(e Y ), is a set of tuples, and Y 1 .OR right.R Y , π X (r) is a projection operation of relation r onto attributes X, δ X (r) is a distinct projection operation of relation r onto attributes X, and ⊙ε{, ←, →, ←→}, wherein represents a join operation, ←→ represents a full outer join operation, ← represents a left outer join operation, and → represents a right outer join operation.
Claim 30
Dependent Claim
268 words
An article of manufacture comprising a computer program carrier embodying one or more instructions of a method of simplifying a query in a computer, the query being performed by the computer to retrieve data from a database stored in a electronic storage device coupled to the computer, the method comprising the steps of: (a) accepting the query into the computer; and (b) replacing a first expression in the query with a second expression, wherein the first expression comprises: π.sub.X.sbsb.1 (e.sub.x)⊙δ.sub.Y.sbsb.1 (e.sub.y) and the second expression comprises: π.sub.X.sbsb.1.sub.Y.sbsb.1 δ.sub.V.sbsb.x.sub.X.sbsb.1.sub.Y.sbsb.1 (e.sub.x ⊙e.sub.y) wherein: e X =(R X , V X , E X ) is a relation, where R X is a non-empty set of real attributes, V X is a non-empty set of virtual attributes, E X , an extension of the relation, also denoted as ext(e X ), is a set of tuples, and X 1 .OR right.R X , e Y =(R Y , V Y , E Y ) is a relation, where R Y is a non-empty set of real attributes, V Y is a non-empty set of virtual attributes, E Y , an extension of the relation, also denoted as ext(e Y ), is a set of tuples, and Y 1 .OR right.R Y , π X (r) is a projection operation of relation r onto attributes X, δ X (r) is a distinct projection operation of relation r onto attributes X, and ⊙ε{, ←, →, ←→}, wherein represents a join operation, ←→ represents a full outer join operation, ← represents a left outer join operation, and → represents a right outer join operation.
Claim 31
Dependent Claim
276 words
An article of manufacture comprising a computer program carrier embodying one or more instructions of a method of simplifying a query in a computer, the query being performed by the computer to retrieve data from a database stored in a electronic storage device coupled to the computer, the method comprising the steps of: (a) accepting the query into the computer; and (b) replacing a first expression in the query with a second expression, wherein the first expression comprises: π.sub.X.sbsb.2 δ.sub.X.sbsb.1 (e.sub.x)⊙π.sub.Y.sbsb.1 (e.sub.y) and the second expression comprises: π.sub.X.sbsb.2.sub.Y.sbsb.1 δ.sub.V.sbsb.y.sub.X.sbsb.1.sub.Y.sbsb.1 (e.sub.x ⊙e.sub.Y) wherein: e X =(R X , V X , E X ) is a relation, where R X is a non-empty set of real attributes, V X is a non-empty set of virtual attributes, E X , an extension of the relation, also denoted as ext(e X ), is a set of tuples, and X 1 .OR right.R X , and X 2 .OR right.X 1 , e Y =(R Y , V Y , E Y ) is a relation, where R Y is a non-empty set of real attributes, V Y is a non-empty set of virtual attributes, E Y , an extension of the relation, also denoted as ext(e Y ), is a set of tuples, and Y 1 .OR right.R Y , π X (r) is a projection operation of relation r onto attributes X, δ X (r) is a distinct projection operation of relation r onto attributes X, and ⊙ε{, ←, →, ←→}, wherein represents a join operation, ←→ represents a full outer join operation, ← represents a left outer join operation, and → represents a right outer join operation.
Claim 32
Dependent Claim
276 words
An article of manufacture comprising a computer program carrier embodying one or more instructions of a method of simplifying a query in a computer, the query being performed by the computer to retrieve data from a database stored in a electronic storage device coupled to the computer, the method comprising the steps of: (a) accepting the query into the computer; and (b) replacing a first expression in the query with a second expression, wherein the first expression comprises: π.sub.X.sbsb.2 δ.sub.X.sbsb.1 (e.sub.x)⊙π.sub.Y.sbsb.1 (e.sub.y) and the second expression comprises: π.sub.X.sbsb.2.sub.Y.sbsb.1 δ.sub.V.sbsb.y.sub.X.sbsb.1.sub.Y.sbsb.1 (e.sub.x ⊙e.sub.Y) wherein: e X =(R X , V X , E X ) is a relation, where R X is a non-empty set of real attributes, V X is a non-empty set of virtual attributes, E X , an extension of the relation, also denoted as ext(e X ), is a set of tuples, and X 1 .OR right.R X , and X 2 .OR right.X 1 , e Y =(R Y , V Y , E Y ) is a relation, where R Y is a non-empty set of real attributes, V Y is a non-empty set of virtual attributes, E Y , an extension of the relation, also denoted as ext(e Y ), is a set of tuples, and Y 1 .OR right.R Y , π X (r) is a projection operation of relation r onto attributes X, δ X (r) is a distinct projection operation of relation r onto attributes X, and ⊙ε{, ←, →, ←→}, wherein represents a join operation, ←→ represents a full outer join operation, ← represents a left outer join operation, and → represents a right outer join operation.
Claim 33
Dependent Claim
276 words
An article of manufacture comprising a computer program carrier embodying one or more instructions of a method of simplifying a query in a computer, the query being performed by the computer to retrieve data from a database stored in a electronic storage device coupled to the computer, the method comprising the steps of: (a) accepting the query into the computer; and (b) replacing a first expression in the query with a second expression, wherein the first expression comprises: π.sub.X.sbsb.2 δ.sub.X.sbsb.1 (e.sub.x)⊙δ.sub.Y.sbsb.1 (e.sub.y) and the second expression comprises: π.sub.X.sbsb.2.sub.Y.sbsb.1 δ.sub.X.sbsb.1.sub.Y.sbsb.1 (e.sub.x ⊙e.sub.Y) wherein: e X =(R X , V X , E X ) is a relation, where R X is a non-empty set of real attributes, V X is a non-empty set of virtual attributes, E X , an extension of the relation, also denoted as ext(e X ), is a set of tuples, and X 1 .OR right.R X , and X 2 .OR right.X 1 , e Y =(R Y , V Y , E Y ) is a relation, where R Y is a non-empty set of real attributes, V Y is a non-empty set of virtual attributes, E Y , an extension of the relation, also denoted as ext(e Y ), is a set of tuples, and Y 1 .OR right.R Y , π X (r) is a projection operation of relation r onto attributes X, δ X (r) is a distinct projection operation of relation r onto attributes X, and ⊙ε{, ←, →, ←→}, wherein represents a join operation, ←→ represents a full outer join operation, ← represents a left outer join operation, and → represents a right outer join operation.
Claim 34
Dependent Claim
276 words
An article of manufacture comprising a computer program carrier embodying one or more instructions of a method of simplifying a query in a computer, the query being performed by the computer to retrieve data from a database stored in a electronic storage device coupled to the computer, the method comprising the steps of: (a) accepting the query into the computer; and (b) replacing a first expression in the query with a second expression, wherein the first expression comprises: π.sub.X.sbsb.2 δ.sub.X.sbsb.1 (e.sub.x)⊙δ.sub.Y.sbsb.1 (e.sub.y) and the second expression comprises: π.sub.X.sbsb.2.sub.Y.sbsb.1 δ.sub.X.sbsb.1.sub.Y.sbsb.1 (e.sub.x ⊙e.sub.Y) wherein: e X =(R X , V X , E X ) is a relation, where R X is a non-empty set of real attributes, V X is a non-empty set of virtual attributes, E X , an extension of the relation, also denoted as ext(e X ), is a set of tuples, and X 1 .OR right.R X , and X 2 .OR right.X 1 , e Y =(R Y , V Y , E Y ) is a relation, where R Y is a non-empty set of real attributes, V Y is a non-empty set of virtual attributes, E Y , an extension of the relation, also denoted as ext(e Y ), is a set of tuples, and Y 1 .OR right.R Y , π X (r) is a projection operation of relation r onto attributes X, δ X (r) is a distinct projection operation of relation r onto attributes X, and ⊙ε{, ←, →, ←→}, wherein represents a join operation, ←→ represents a full outer join operation, ← represents a left outer join operation, and → represents a right outer join operation.
Claim 35
Dependent Claim
276 words
An article of manufacture comprising a computer program carrier embodying one or more instructions of a method of simplifying a query in a computer, the query being performed by the computer to retrieve data from a database stored in a electronic storage device coupled to the computer, the method comprising the steps of: (a) accepting the query into the computer; and (b) applying an identity to the query, wherein the identity comprises: δ.sub.X.sbsb.1.sub.Y.sbsb.1 (e.sub.x ⊙.sup.p.sbsp.xy e.sub.y)=δ.sub.X.sbsb.1 (e.sub.x).sub.⊙.sup.p.sbsp.xy δ.sub.Y.sbsb.1 (e.sub.y) and wherein: e X =(R X , V X , E X ) is a relation, where R X is a non-empty set of real attributes, V X is a non-empty set of virtual attributes, E X , an extension of the relation, also denoted as ext(e X ), is a set of tuples, and X 1 .OR right.R X , e Y =(R Y , V Y , E Y ) is a relation, where R Y is a non-empty set of real attributes, V Y is a non-empty set of virtual attributes, E Y , an extension of the relation, also denoted as ext(e Y ), is a set of tuples, and Y 1 .OR right.R Y , p xy is a predicate, sch(p xy ) is a schema of p xy , (sch(p xy )∩R X ).OR right.X 1 , (sch(p xy )∩R Y ).OR right.Y 1 , δ X (r) is a distinct projection operation of relation r onto attributes X, and ⊙ε{, ←, →, ←→}, wherein represents a join operation, ←→ represents a full outer join operation, ← represents a left outer join operation, and → represents a right outer join operation.
Claim 36
Dependent Claim
276 words
An article of manufacture comprising a computer program carrier embodying one or more instructions of a method of simplifying a query in a computer, the query being performed by the computer to retrieve data from a database stored in a electronic storage device coupled to the computer, the method comprising the steps of: (a) accepting the query into the computer; and (b) applying an identity to the query, wherein the identity comprises: δ.sub.X.sbsb.1.sub.Y.sbsb.1 (e.sub.x ⊙.sup.p.sbsp.xy e.sub.y)=δ.sub.X.sbsb.1 (e.sub.x).sub.⊙.sup.p.sbsp.xy δ.sub.Y.sbsb.1 (e.sub.y) and wherein: e X =(R X , V X , E X ) is a relation, where R X is a non-empty set of real attributes, V X is a non-empty set of virtual attributes, E X , an extension of the relation, also denoted as ext(e X ), is a set of tuples, and X 1 .OR right.R X , e Y =(R Y , V Y , E Y ) is a relation, where R Y is a non-empty set of real attributes, V Y is a non-empty set of virtual attributes, E Y , an extension of the relation, also denoted as ext(e Y ), is a set of tuples, and Y 1 .OR right.R Y , p xy is a predicate, sch(p xy ) is a schema of p xy , (sch(p xy )∩R X ).OR right.X 1 , (sch(p xy )∩R Y ).OR right.Y 1 , δ X (r) is a distinct projection operation of relation r onto attributes X, and ⊙ε{, ←, →, ←→}, wherein represents a join operation, ←→ represents a full outer join operation, ← represents a left outer join operation, and → represents a right outer join operation.
References Cited (Backward Citations)
US4829427A
Cited
US4769772A
Cited
US5091852A
Cited
US5335345A
Cited
US5367675A
Cited
US5495605A
Cited
US5412806A
Cited
USPTO Annuity & Maintenance Windows
| Annuity Stage | Window Opens | Payment Deadline | Surcharge Period Until | Estimated Fee | Status |
|---|---|---|---|---|---|
| 3.5 Years (Year 4) | 2001-12-28 | 2002-06-29 | 2002-12-29 | $2000.00 | Window Closed / Lapsed |
| 7.5 Years (Year 8) | 2005-12-28 | 2006-06-29 | 2006-12-29 | $3760.00 | Window Closed / Lapsed |
| 11.5 Years (Year 12) | 2009-12-28 | 2010-06-29 | 2010-12-29 | $7700.00 | Window Closed / Lapsed |