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US5557791A Expired / Lapsed US ⏱️ 0.0 years remaining

Outer join operations using responsibility regions assigned to inner tables in a relational database

Assignee: International Business Machines Corp
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Filing: 1994-10-19
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Granted: 1996-09-17
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Expires: 2014-10-19
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Abstract

Abstract A computer database system utilizes a method for performing a right outer join of database tables without sorting the inner table (T2). The processing of each tuple in the outer table (T1) includes the preservation in the joint output of all tuples in T2 which are in its responsibility region. The initialization step of the process preserves in the join output all of the tuples in T2 which have column set values less than the lowest column set value in T1, i.e. the first tuple in T1, since T1 is sorted or accessed using a sorted index. The responsibility region for tuples in T1, other than the last tuple, is defined as those tuples which have column set values less than the column set value for the next tuple in T1 and greater than or equal to the column set value for the current T1 tuple. The last tuple in T1 must preserve all of the tuples in T2 which have not already been preserved in T2, i.e. all tuples greater than or equal to its column set value. If T1 has duplicate values for the column set value, only the last one preserves the associated T2 tuples. Additional methods for parallel execution of the outer join methods and methods for applying the outer join methods to subqueries (i.e., an All (or universal) Right Join (ARJOIN) and an Existential Right Join (ERJOIN)) are described.

Inventors

  • 👤 Josephine M. Cheng
  • 👤 Chandrasekaran Mohan
  • 👤 Mir H. Pirahesh

Bibliographic Details

Application Number —
Jurisdiction US
Data Source google_patents
Last Synchronized 2026-10-26 22:16
CPC Classifications
G; G06; G06F; G06F16/00; G06F16/20; G06F16/24; G06F16/245; G06F16/2455; G06F16/24553; G06F16/24558; G06F16/2456; Y; Y10; Y10S; Y10S707/00; Y10S707/99931; Y10S707/99932

Claims Analysis

Total Claims: 39
Claim 1
Independent Claim 162 words
An improved method of performing a fight outer join with specified join predicates in a computerized database system having an inner table and an outer table, each of which tables is composed of a plurality of tuples having multiple columns, the outer table being ordered or indexed in a sorted sequence on a selected set of columns, the improvement comprising the steps of: (a) determining a plurality of responsibility regions in the inner table using a selected set of columns such that every tuple in the inner table belongs to one and only one responsibility region; and (b) processing each responsibility region by outputting all tuples of the inner table which belong to the responsibility region, wherein if an inner tuple and an outer tuple match by satisfying all the specified join predicates, outputting the outer tuple with the inner tuple, and if the inner and outer tuples do not match, outputting null values for the outer tuple with the inner tuple.
Claim 2
Dependent Claim 162 words
An improved method of performing a fight outer join with specified join predicates in a computerized database system having an inner table and an outer table, each of which tables is composed of a plurality of tuples having multiple columns, the outer table being ordered or indexed in a sorted sequence on a selected set of columns, the improvement comprising the steps of: (a) determining a plurality of responsibility regions in the inner table using a selected set of columns such that every tuple in the inner table belongs to one and only one responsibility region; and (b) processing each responsibility region by outputting all tuples of the inner table which belong to the responsibility region, wherein if an inner tuple and an outer tuple match by satisfying all the specified join predicates, outputting the outer tuple with the inner tuple, and if the inner and outer tuples do not match, outputting null values for the outer tuple with the inner tuple.
Claim 3
Dependent Claim 48 words
The method of claim 1 wherein the processing step further comprises the step of outputting all tuples of the inner table which have values of a selected set of columns less than the value of the selected set of columns for a first tuple of the outer table.
Claim 4
Dependent Claim 51 words
The method of claim 1 wherein the processing step further comprises the step of outputting all tuples of the inner table which have values of a selected set of columns equal to or greater than the value of the selected set of columns for a last tuple of the outer table.
Claim 5
Dependent Claim 175 words
The method of claim 1 wherein the processing step further comprises the steps of: (a) sequencing through the tuples in the outer table referencing a current tuple and a next tuple and for each unique set of column values in the outer table, other than that of a last tuple, accessing a set of tuples from the inner table which corresponds to all tuples in the inner table which have values of the selected set of columns greater than or equal to the value of the selected set of columns for the current tuple of the outer table and less than the value of a specified set of columns for the next tuple of the outer table; and (b) for the last tuple in the outer table accessing a set of tuples of the inner table which corresponds to all tuples in the inner table which have values of the selected set of columns greater than or equal to the value of the selected set of columns for the last tuple of the outer table.
Claim 6
Dependent Claim 23 words
The method of claim 1 wherein the determining step further comprises the step of defining both null responsibility regions and non-null responsibility regions.
Claim 7
Dependent Claim 34 words
The method of claim 5 wherein the join to be performed is an existential right join, and the processing step further comprises the step of accessing the inner table only for non-null responsibility regions.
Claim 8
Dependent Claim 48 words
The method of claim 5 wherein the join to be performed is an all right join having an ON clause and the processing step further comprises the step of accessing the inner table only for non-null responsibility regions and only for tuples not matched by the ON clause.
Claim 9
Dependent Claim 211 words
An improved method of performing a fight outer join with specified join predicates in a computerized database system having an inner table and an outer table, each of which tables is composed of a plurality of tuples having multiple columns, the outer table being ordered or indexed in a sorted sequence on a selected set of columns, the improvement comprising the steps of: (a) determining a plurality of responsibility regions in the inner table using a selected set of columns such that every tuple in the inner table belongs to one and only one responsibility region; and (b) processing each responsibility region by outputting all tuples of the inner table which belong to the responsibility region, wherein if an inner tuple and an outer tuple match by satisfying all the specified join predicates, outputting the outer tuple with the inner tuple, and if the inner and outer tuples do not match, outputting null values for the outer tuple with the inner tuple, wherein the determining step further comprises the step of defining an initial responsibility region which contains all tuples of the inner table which have values of a selected set of columns less than the value of the selected set of columns for a first tuple of the outer table.
Claim 10
Dependent Claim 211 words
An improved method of performing a fight outer join with specified join predicates in a computerized database system having an inner table and an outer table, each of which tables is composed of a plurality of tuples having multiple columns, the outer table being ordered or indexed in a sorted sequence on a selected set of columns, the improvement comprising the steps of: (a) determining a plurality of responsibility regions in the inner table using a selected set of columns such that every tuple in the inner table belongs to one and only one responsibility region; and (b) processing each responsibility region by outputting all tuples of the inner table which belong to the responsibility region, wherein if an inner tuple and an outer tuple match by satisfying all the specified join predicates, outputting the outer tuple with the inner tuple, and if the inner and outer tuples do not match, outputting null values for the outer tuple with the inner tuple, wherein the determining step further comprises the step of defining an initial responsibility region which contains all tuples of the inner table which have values of a selected set of columns less than the value of the selected set of columns for a first tuple of the outer table.
Claim 11
Dependent Claim 214 words
An improved method of performing a right outer join with specified join predicates in a computerized database system having an inner table and an outer table, each of which tables is composed of a plurality of tuples having multiple columns, the outer table being ordered or indexed in a sorted sequence on a selected set of columns, the improvement comprising the steps of: (a) determining a plurality of responsibility regions in the inner table using a selected set of columns such that every tuple in the inner table belongs to one and only one responsibility region; and (b) processing each responsibility region by outputting all tuples of the inner table which belong to the responsibility region, wherein if an inner tuple and an outer tuple match by satisfying all the specified join predicates, outputting the outer tuple with the inner tuple, and if the inner and outer tuples do not match, outputting null values for the outer tuple with the inner tuple, wherein the determining step further comprises the step of defining a final responsibility region which contains all tuples of the inner table which have values of a selected set of columns equal to or greater than the value of the selected set of columns for a last tuple of the outer table.
Claim 12
Dependent Claim 214 words
An improved method of performing a right outer join with specified join predicates in a computerized database system having an inner table and an outer table, each of which tables is composed of a plurality of tuples having multiple columns, the outer table being ordered or indexed in a sorted sequence on a selected set of columns, the improvement comprising the steps of: (a) determining a plurality of responsibility regions in the inner table using a selected set of columns such that every tuple in the inner table belongs to one and only one responsibility region; and (b) processing each responsibility region by outputting all tuples of the inner table which belong to the responsibility region, wherein if an inner tuple and an outer tuple match by satisfying all the specified join predicates, outputting the outer tuple with the inner tuple, and if the inner and outer tuples do not match, outputting null values for the outer tuple with the inner tuple, wherein the determining step further comprises the step of defining a final responsibility region which contains all tuples of the inner table which have values of a selected set of columns equal to or greater than the value of the selected set of columns for a last tuple of the outer table.
Claim 13
Dependent Claim 269 words
An improved method of performing a right outer join in a computerized database system having an inner table and an outer table, each of which tables is composed of a plurality of tuples having multiple columns, the outer table being ordered or indexed in a sorted sequence on a selected set of columns, the improvement comprising the steps of: (a) determining a plurality of responsibility regions in the inner table using a selected set of columns such that every tuple in the inner table belongs to one and only one responsibility region, wherein the determining step further comprises the steps of: sequencing through the tuples in the outer table referencing a current tuple and a next tuple and for each unique set of column values in the outer table, other than that of a last tuple, assigning one of the plurality of responsibility regions to include a set of tuples from the inner table which corresponds to all tuples in the inner table which have values of the selected set of columns greater than or equal to the value of the selected set of columns for the current tuple of the outer table and less than the value of the specified set of columns for the next tuple of the outer table, and for the last tuple in the outer table, assigning a last responsibility region to include all tuples from the inner table which have not been assigned to any other one of the plurality of responsibility regions; and (b) processing each responsibility region by outputting all tuples of the inner table which belong to the responsibility region.
Claim 14
Dependent Claim 269 words
An improved method of performing a right outer join in a computerized database system having an inner table and an outer table, each of which tables is composed of a plurality of tuples having multiple columns, the outer table being ordered or indexed in a sorted sequence on a selected set of columns, the improvement comprising the steps of: (a) determining a plurality of responsibility regions in the inner table using a selected set of columns such that every tuple in the inner table belongs to one and only one responsibility region, wherein the determining step further comprises the steps of: sequencing through the tuples in the outer table referencing a current tuple and a next tuple and for each unique set of column values in the outer table, other than that of a last tuple, assigning one of the plurality of responsibility regions to include a set of tuples from the inner table which corresponds to all tuples in the inner table which have values of the selected set of columns greater than or equal to the value of the selected set of columns for the current tuple of the outer table and less than the value of the specified set of columns for the next tuple of the outer table, and for the last tuple in the outer table, assigning a last responsibility region to include all tuples from the inner table which have not been assigned to any other one of the plurality of responsibility regions; and (b) processing each responsibility region by outputting all tuples of the inner table which belong to the responsibility region.
Claim 15
Dependent Claim 218 words
An improved method of performing a right outer join in a computerized database system having an inner table and an outer table, each of which tables is composed of a plurality of tuples having multiple columns, the outer table being ordered in a sorted sequence on a selected set of columns, the improvement comprising the steps of: (a) outputting all tuples of the inner table which have values of a selected set of columns less than a value of a selected set of columns for a first tuple of the outer table; (b) sequencing through the tuples in the outer table referencing a current tuple and a next tuple and for each unique set of column values in the outer table, other than that of a last tuple, outputting a set of tuples from the inner table which corresponds to all tuples in the inner table which have values of the selected set of columns greater than or equal to the value of the selected set of columns for the current tuple of the outer table and less than the value of a specified set of columns for the next tuple of the outer table; and (c) for the last tuple in the outer table outputting all tuples from the inner table which have not been previously output.
Claim 16
Dependent Claim 218 words
An improved method of performing a right outer join in a computerized database system having an inner table and an outer table, each of which tables is composed of a plurality of tuples having multiple columns, the outer table being ordered in a sorted sequence on a selected set of columns, the improvement comprising the steps of: (a) outputting all tuples of the inner table which have values of a selected set of columns less than a value of a selected set of columns for a first tuple of the outer table; (b) sequencing through the tuples in the outer table referencing a current tuple and a next tuple and for each unique set of column values in the outer table, other than that of a last tuple, outputting a set of tuples from the inner table which corresponds to all tuples in the inner table which have values of the selected set of columns greater than or equal to the value of the selected set of columns for the current tuple of the outer table and less than the value of a specified set of columns for the next tuple of the outer table; and (c) for the last tuple in the outer table outputting all tuples from the inner table which have not been previously output.
Claim 17
Dependent Claim 46 words
The method of claim 11 further comprising the steps of: (a) partitioning the outer table into a plurality of partitions based on ordering by column values; (b) assigning the partitions of the outer table to a plurality of tasks; and (c) running the tasks in parallel.
Claim 18
Dependent Claim 40 words
The method of claim 12 further comprising the steps of: (a) creating a plurality of accessing tasks associated with each of the tasks which perform the function of accessing the inner table; and (b) running the accessing tasks in parallel.
Claim 19
Dependent Claim 50 words
The method of claim 11 wherein step (c) further comprises the step of outputting all tuples of the inner table which have values of the selected set of columns greater than or equal to the value of the specified set of columns for the last tuple of the outer table.
Claim 20
Dependent Claim 238 words
An improved computerized database system having means for performing a fight outer join, an existential fight join, and an all right join on an inner table and an outer table, each table composed of a plurality of tuples having multiple columns, the outer table being ordered or indexed in a sorted sequence on a selected set of columns, and wherein specified join predicates are associated with the right outer join, the existential fight join, and the all right join, the improvement comprising: (a) means for determining a plurality of responsibility regions in the inner table using the selected set of columns such that every tuple in the inner table belongs to one and only one responsibility region; (b) means for processing each responsibility region by outputting all tuples of the inner table which belong to the responsibility region, wherein for the right outer join, if an inner tuple and an outer tuple match by satisfying all the associated specified join predicates, outputting the outer tuple with the inner tuple, and if the inner and outer tuples do not match, outputting null values for the outer tuple with the inner tuple, for the existential fight join, if the inner and outer tuples match, outputting the inner tuple once, and for the all right join, if the inner and outer tuples do not match, outputting the inner tuple, wherein said means perform the join operations without sorting the inner table.
Claim 21
Dependent Claim 238 words
An improved computerized database system having means for performing a fight outer join, an existential fight join, and an all right join on an inner table and an outer table, each table composed of a plurality of tuples having multiple columns, the outer table being ordered or indexed in a sorted sequence on a selected set of columns, and wherein specified join predicates are associated with the right outer join, the existential fight join, and the all right join, the improvement comprising: (a) means for determining a plurality of responsibility regions in the inner table using the selected set of columns such that every tuple in the inner table belongs to one and only one responsibility region; (b) means for processing each responsibility region by outputting all tuples of the inner table which belong to the responsibility region, wherein for the right outer join, if an inner tuple and an outer tuple match by satisfying all the associated specified join predicates, outputting the outer tuple with the inner tuple, and if the inner and outer tuples do not match, outputting null values for the outer tuple with the inner tuple, for the existential fight join, if the inner and outer tuples match, outputting the inner tuple once, and for the all right join, if the inner and outer tuples do not match, outputting the inner tuple, wherein said means perform the join operations without sorting the inner table.
Claim 22
Dependent Claim 137 words
The system of claim 15 further comprising: (a) means for sequencing through the tuples in the outer table referencing a current tuple and a next tuple and for each unique set of column values in the outer table, other than that of a last tuple, outputting a set of tuples from the inner table which correspond to all tuples in the inner table which have values of the selected set of columns greater than or equal to the value of the selected set of columns for the current tuple of the outer table and less than the value of a specified set of columns for the next tuple of the outer table; and (b) means for outputting for the last tuple in the outer table all tuples from the inner table which have not been previously output.
Claim 23
Dependent Claim 23 words
The system of claim 15 wherein the means for determining further comprises means for defining both null responsibility regions and non-null responsibility regions.
Claim 24
Dependent Claim 34 words
The system of claim 17 wherein the join to be performed is an existential right join, and the means for processing further comprises means for accessing the inner table only for non-null responsibility regions.
Claim 25
Dependent Claim 48 words
The system of claim 17 wherein the join to be performed is an all right join having an ON clause and the means for processing further comprises means for accessing the inner table only for non-null responsibility regions and only for tuples not matched by the ON clause.
Claim 26
Dependent Claim 397 words
An improved computerized database system having means for performing a fight outer join, an existential fight join, and an all right join on an inner table and an outer table, each table composed of a plurality of tuples having multiple columns, the outer table being ordered or indexed in a sorted sequence on a selected set of columns, and wherein specified join predicates are associated with the right outer join, the existential fight join, and the all fight join, the improvement comprising: (a) means for determining a plurality of responsibility regions in the inner table using the selected set of columns such that every tuple in the inner table belongs to one and only one responsibility region, wherein the means for determining further comprises: means for sequencing through the tuples in the outer table referencing a current tuple and a next tuple and for each unique set of column values in the outer table, other than that of a last tuple, assigning one of the plurality of responsibility regions to include a set of tuples from the inner table which corresponds to all tuples in the inner table which have values of the selected set of columns greater than or equal to the value of the selected set of columns for the current tuple of the outer table and less than the value of the specified set of columns for the next tuple of the outer table, and means for assigning a responsibility region for the last tuple in the outer table to include all tuples from the inner table which have not been assigned to any other one of the plurality of responsibility regions; and (b) means for processing each responsibility region by outputting all tuples of the inner table which belong to the responsibility region, wherein for the right outer join, if an inner tuple and an outer tuple match by satisfying all the associated specified join predicates, outputting the outer tuple with the inner tuple, and if the inner and outer tuples do not match, outputting null values for the outer tuple with the inner tuple, for the existential fight join, if the inner and outer tuples match, outputting the inner tuple once, and for the all fight join, if the inner and outer tuples do not match, outputting the inner tuple, wherein said means perform the join operations without sorting the inner table.
Claim 27
Dependent Claim 397 words
An improved computerized database system having means for performing a fight outer join, an existential fight join, and an all right join on an inner table and an outer table, each table composed of a plurality of tuples having multiple columns, the outer table being ordered or indexed in a sorted sequence on a selected set of columns, and wherein specified join predicates are associated with the right outer join, the existential fight join, and the all fight join, the improvement comprising: (a) means for determining a plurality of responsibility regions in the inner table using the selected set of columns such that every tuple in the inner table belongs to one and only one responsibility region, wherein the means for determining further comprises: means for sequencing through the tuples in the outer table referencing a current tuple and a next tuple and for each unique set of column values in the outer table, other than that of a last tuple, assigning one of the plurality of responsibility regions to include a set of tuples from the inner table which corresponds to all tuples in the inner table which have values of the selected set of columns greater than or equal to the value of the selected set of columns for the current tuple of the outer table and less than the value of the specified set of columns for the next tuple of the outer table, and means for assigning a responsibility region for the last tuple in the outer table to include all tuples from the inner table which have not been assigned to any other one of the plurality of responsibility regions; and (b) means for processing each responsibility region by outputting all tuples of the inner table which belong to the responsibility region, wherein for the right outer join, if an inner tuple and an outer tuple match by satisfying all the associated specified join predicates, outputting the outer tuple with the inner tuple, and if the inner and outer tuples do not match, outputting null values for the outer tuple with the inner tuple, for the existential fight join, if the inner and outer tuples match, outputting the inner tuple once, and for the all fight join, if the inner and outer tuples do not match, outputting the inner tuple, wherein said means perform the join operations without sorting the inner table.
Claim 28
Dependent Claim 140 words
An improved method of performing an existential right join with specified join predicates in a computerized database system having an inner table and an outer table, each of which tables are composed of a plurality of tuples having multiple columns, the outer table being ordered or indexed in a sorted sequence on a selected set of columns, the improvement comprising the steps of: (a) determining a plurality of responsibility regions in the inner table using a selected set of columns such that every tuple in the inner table belongs to one and only one responsibility region; and (b) processing each non-null responsibility region by outputting all tuples of the inner table which belong to the non-null responsibility region, wherein if an inner tuple and an outer tuple match by satisfying all the specified join predicates, outputting the inner tuple once.
Claim 29
Dependent Claim 140 words
An improved method of performing an existential right join with specified join predicates in a computerized database system having an inner table and an outer table, each of which tables are composed of a plurality of tuples having multiple columns, the outer table being ordered or indexed in a sorted sequence on a selected set of columns, the improvement comprising the steps of: (a) determining a plurality of responsibility regions in the inner table using a selected set of columns such that every tuple in the inner table belongs to one and only one responsibility region; and (b) processing each non-null responsibility region by outputting all tuples of the inner table which belong to the non-null responsibility region, wherein if an inner tuple and an outer tuple match by satisfying all the specified join predicates, outputting the inner tuple once.
Claim 30
Dependent Claim 164 words
The method of claim 21 wherein the determining step further comprises the steps of: (a) sequencing through the tuples in the outer table referencing a current tuple and a next tuple and for each unique set of column values in the outer table, other than that of a last tuple, assigning one of the plurality of responsibility regions to include a set of tuples from the inner table which corresponds to all tuples in the inner table which have values of the selected set of columns greater than or equal to the value of the selected set of columns for the current tuple of the outer table and less than the value of the specified set of columns for the next tuple of the outer table; and (b) for the last tuple in the outer table, assigning a last responsibility region to include all tuples from the inner table which have not been assigned to any other one of the plurality of responsibility regions.
Claim 31
Dependent Claim 74 words
The method of claim 21 wherein the processing step further comprises the steps of: (a) sequencing through the tuples in the outer table referencing a non-null responsibility region and accessing a set of tuples from the inner table which corresponds to all tuples in the inner table which have values of the selected set of columns equal to the value of the selected set of columns for the current tuple of the outer table.
Claim 32
Dependent Claim 142 words
An improved method of performing an all right join with specified join predicates in a computerized database system having an inner table and an outer table, each of which tables are composed of a plurality of tuples having multiple columns, the outer table being ordered or indexed in a sorted sequence on a selected set of columns, the improvement comprising the steps of: (a) determining a plurality of responsibility regions in the inner table using a selected set of columns such that every tuple in the inner table belongs to one and only one responsibility region; and (b) processing each non-null responsibility region by outputting all tuples of the inner table which belong to the non-null responsibility region, wherein if an inner tuple and an outer tuple do not match by not satisfying all the specified join predicates, outputting the inner tuple.
Claim 33
Dependent Claim 142 words
An improved method of performing an all right join with specified join predicates in a computerized database system having an inner table and an outer table, each of which tables are composed of a plurality of tuples having multiple columns, the outer table being ordered or indexed in a sorted sequence on a selected set of columns, the improvement comprising the steps of: (a) determining a plurality of responsibility regions in the inner table using a selected set of columns such that every tuple in the inner table belongs to one and only one responsibility region; and (b) processing each non-null responsibility region by outputting all tuples of the inner table which belong to the non-null responsibility region, wherein if an inner tuple and an outer tuple do not match by not satisfying all the specified join predicates, outputting the inner tuple.
Claim 34
Dependent Claim 55 words
The method of claim 24 wherein the determining step further comprises the step of defining an initial non-null responsibility region which contains all tuples of the inner table which have values of a selected set of columns less than the value of the selected set of columns for a first tuple of the outer table.
Claim 35
Dependent Claim 58 words
The method of claim 24 wherein the determining step further comprises the step of defining a final non-null responsibility region which contains all tuples of the inner table which have values of a selected set of columns equal to or greater than the value of the selected set of columns for a last tuple of the outer table.
Claim 36
Dependent Claim 48 words
The method of claim 24 wherein the processing step further comprises the step of outputting all tuples of the inner table which have values of a selected set of columns less than the value of the selected set of columns for a first tuple of the outer table.
Claim 37
Dependent Claim 52 words
The method of claim 24 wherein the processing step further comprises the step of outputting all tuples of the inner table which have values of a selected set of columns greater than and not equal to the value of the selected set of columns for a last tuple of the outer table.
Claim 38
Dependent Claim 167 words
The method of claim 24 wherein the determining step further comprises the steps of: (a) sequencing through the tuples in the outer table referencing a current tuple and a next tuple and for each unique set of column values in the outer table, other than that of a last tuple, assigning one of the plurality of non-null responsibility regions to include a set of tuples from the inner table which corresponds to all tuples in the inner table which have values of the selected set of columns greater than or equal to the value of a selected set of columns for the current tuple of the outer table and less than the value of the specified set of columns for the next tuple of the outer table; and (b) for the last tuple in the outer table, assigning a last non-null responsibility region to include all tuples from the inner table which have not been assigned to any other one of the plurality of non-null responsibility regions.
Claim 39
Dependent Claim 177 words
The method of claim 24 wherein the processing step further comprises the steps of: (a) sequencing through the tuples in the outer table referencing a current tuple and a next tuple and for each unique set of column values in the outer table, other than that of a last tuple, accessing a set of tuples from the inner table which corresponds to all tuples in the inner table which have values of the selected set of columns greater than and not equal to the value of the selected set of columns for the current tuple of the outer table and less than the value of a specified set of columns for the next tuple of the outer table; and (b) for the last tuple in the outer table accessing a set of tuples of the inner table which corresponds to all tuples in the inner table which have values of the selected set of columns greater than and not equal to the value of the selected set of columns for the last tuple of the outer table.

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