Abstract:
A technique is provided for incrementally maintaining column cardinality estimates in database management systems. The system catalog table containing a cardinality estimate for a column is extended to include an appropriate data structure. A modified linear counting technique is used in a first embodiment of a method for column cardinality estimation. Moreover, a modified logarithmic counting technique is used in a second, preferred embodiment of a column cardinality estimation method to reduce storage requirements for the data structure. The cardinality estimate is produced by an initial scan of the data but is then further maintained without requiring a full scan of the data. Data changes are reflected incrementally in modifications to the initial cardinality estimate, keeping the cardinality statistics more current with respect to the database condition. The technique of the invention typically provides a capability for a database management system to produce more efficient search plans providing more effective responses to user queries through the use of improved cardinality statistics.

Description:
FIELD OF THE INVENTION 
   This invention generally relates to determining frequent data values within a set of data values and more particularly to incrementally maintaining statistics such as, column cardinality, in relational database systems. 
   BACKGROUND OF THE INVENTION 
   To ensure generation of an efficient query plan, a database management system typically includes a query optimization software module. The query optimization software module generates search plans for query requests based on optimization rules that consider, among many variables, the size of the response set (amount of data expected to be returned) and the number of unique values within the data being queried. 
   Current, accurate database statistics are highly desired by performance sensitive query software modules (for example, a query optimizer) of database management systems. When database statistics are inaccurate or no longer current, the query optimizer is most likely to generate inefficient query plans. Inefficient query plans perform poorly at run time degrading overall performance of the database management system. 
   In the following simple examples the actual cardinality value and the estimated cardinality value are equivalent, which may not be the typical case. 
   Column cardinality is an example of an important database statistic. Column cardinality is a value representing the number of distinct values found in a database column. For example, the column cardinality of the NAME column in Table  1 A of  FIG. 2A  is three, because there are three unique values (names) in the column. Column cardinality statistics (number of unique values within a set of values) are among some of the most commonly required statistics used by a query optimization software module. Column cardinality statistics are used in conjunction with other statistics to compute query plan resource consumption estimates which are then used in determining the most efficient plan for a given query. 
   Typical database systems estimate column cardinality because exact computation is too expensive in terms of time and resource and due to the dynamic nature of the value. In many commercial database systems, statistics collection is a batch operation, allowing the statistics processing workload to be scheduled based on database performance needs. Typically, database statistics represent a snapshot of the data only for the instant the statistics are generated. As a database table changes, previously computed statistics, associated with that table, may no longer be representative of the current state of the table and its indexes. Statistics for a table should be recalculated to reflect the current state of the table. 
   It is typically a simple task to incrementally maintain basic statistics such as the total number of rows in a table. However, column cardinality estimates are usually more difficult to maintain. Current techniques for maintaining estimates of column cardinality require rescanning the entire column as the data in that column changes. For example, assume a column “C” initially contains twenty distinct values and subsequently thirty additional distinct values are inserted. Computing a new estimate of column cardinality for column “C” by simply adding the cardinality of the two data sets may lead to an incorrect result due to duplicate entries. An allowance has to be made for duplicate values within the combined set of old and new values. 
   For example, consider Table  1 A ( FIG. 2A ), EMPLOYEE, containing employee information which has two columns, one being NAME and the other SALARY. 
   The column NAME has the following four values: “smith”, “jones”, “doole”, and “smith”. Observe that the value “smith” is repeated twice, therefore, the estimated column cardinality value of column NAME is equal to “3”. This is because there are only three distinct values namely, “smith”, “jones”, and “doole”. On the other hand the estimated column cardinality value of the column SALARY is equal to “4” because all values in this column are distinct. 
   A typical database system has at least one method of computing column cardinality estimates. Typical examples of such methods are Linear counting and Logarithmic counting, both of which are well known to persons of ordinary skill in the art. When a database system computes an estimate of column cardinality, the database system stores the estimated value in what is known as a system catalog table for future use by the database system. For example, in a typical database system, the system catalog table that stores the column cardinality estimates for data in Table  1 A of  FIG. 2A  may be as represented by Table  1 B of  FIG. 2B . 
   Table  1 B ( FIG. 2B ), shows the column cardinality estimate of the column NAME belonging to table EMPLOYEE is “3” and the column cardinality estimate of the column SALARY belonging to table EMPLOYEE is “4”. 
   In a typical database system, a query optimizer (a component of the database system) then obtains the values of the column cardinality estimates from a database system catalog table. The query optimizer then uses the column cardinality values along with other statistics when computing the resource consumption estimates for a given set of database queries. 
   Consider once again the table Employee shown in Table  1 A ( FIG. 2A ). A new row is added to Table  1 A ( FIG. 2A ) to represent an employee called “harris” with a salary “200,000”. The updated table Employee is now depicted in Table  2 A of  FIG. 2C . 
   Computing a new column cardinality estimate value for the column NAME for example, according to current methods applied by database systems, requires reading all the NAME values; smith, jones, doole, smith, and harris. 
   After computing the cardinality estimates for both columns of the recently updated table in Table  2 A ( FIG. 2C ), the database manager updates the system catalog table, as now shown in Table  2 B of  FIG. 2D . 
   The content of the database system catalog table in Table  2 B ( FIG. 2D ) indicates that the new column cardinality estimate of the column NAME in table EMPLOYEE is “4”and the new column cardinality estimate of the column SALARY in the same table is “4” as well. Inserting the new row (“harris”), caused the column cardinality estimate of column NAME to change from “3” to “4”. The column cardinality estimate of column SALARY did not change, remaining at “4” because the added salary value “200,000” is a duplicate of an existing salary value. In practice, where columns may comprise millions of rows, computing the column cardinality exactly requires too much time and computer memory, and so the column cardinality must be estimated. 
   In a “linear counting” technique used to estimate column cardinality, a hashing function is used to transform each data value to a bit string that represents a position in a bit map. Initially all positions in the bit map contain zeros. Hashing a data value to a position in the bit map causes a value at the position to be set to one. A value of zero in a position of the bit map indicates there were no data values that hashed to that position. A value of one in a position in the bit map indicates that at least one data value hashed to that position. All data values in the column are hashed, and then the number of distinct data values is estimated by counting the number of bits in the bit map that are set to one (non-zero). Not all data values that hash to the same address are necessarily duplicates. Distinct values that hash to the same location are collisions. Collisions require the count to be adjusted using an adjustment formula, derived using probabilistic techniques (known to those of ordinary skill in the art). 
   Another well known estimation technique is “logarithmic counting.” Although more complicated than linear counting, the bit map used by logarithmic counting is much smaller than that used by linear counting. In logarithmic counting, a hashing function is used to transform each data value to a bit string, which is then further transformed by retaining the leftmost “1” position and converting all remaining positions to “0”. All data values in the column are doubly transformed to bit strings in this manner, and a final bit map is computed as the bit-wise “OR” of all the bit strings for the column. The leftmost “0” position in the final bit map is then computed, and this relative position number n is used to calculate the estimated cardinality value using the formula 2n/q, where “q” is set to a value “0.7735”. This latter expression is a well known probabilistic estimation formula that ensures statistically reasonable results. 
   As can be seen from the foregoing discussion, current cardinality estimation techniques typically require all data values in a column to be obtained each time a new estimate of that column&#39;s cardinality is requested. The detailed example shown previously illustrates a case where a new value was added, but the same requirement also holds for cases where an existing value is deleted or updated. The presence of duplicate entries in columns of data make it difficult to maintain the column cardinality estimates each time data values change. It is apparent, from the examples described, that there is a need for improved efficiency, or expediency or both regarding generation of database management systems statistics. 

   
     DESCRIPTION OF THE DRAWINGS 
     Embodiments of the current invention are described by way of example, in the accompanying drawings in which: 
       FIG. 1  is a block diagram showing a data processing system incorporating an embodiment of the invention; 
       FIGS. 2A through 2K  depict sample database tables used in explanatory examples; 
       FIG. 3  is a flow diagram showing a view of the column cardinality estimation process used in embodiments of the current invention in  FIG. 1 ; 
       FIG. 4  is a block diagram showing a view of the column cardinality estimation process in an embodiment of the invention of  FIG. 3 ; and 
       FIG. 5  is a block diagram showing a view of the column cardinality estimation process in a preferred embodiment of the invention of  FIG. 3 . 
   

   SUMMARY OF THE INVENTION 
   The present invention provides a technique for incrementally updating or maintaining column cardinality estimate values in database management systems. The invention extends the system catalog table storing a column cardinality estimate to also include an appropriate data structure associated with the column for which cardinality is being maintained. The data structure consists of an array of counts, where the interpretation of the counts depends on the particular embodiment. The invention uses the information in the extended data structure in conjunction with a modified counting technique and is suitable for use in database management systems requiring current column statistics. 
   In a first aspect of the invention there is provided a method performed on a computer system for estimating a cardinality value for a set of data values comprising, initializing a data structure for representing counts, obtaining a data value from the set of data values and transforming the data value into a transformed string. Next modifying the data structure with the transformed string and obtaining a summary statistic value from said modified data structure. Finally generating an estimated cardinality value using the summary statistic value. 
   In a another aspect of the invention there is provided a computer system for estimating a cardinality value for a set of data values comprising, means for initializing a data structure for representing counts, means for obtaining a data value from the set of data values and means for transforming the data value into a transformed string. In addition, providing means for modifying data structure with the transformed string, and means for obtaining a summary statistic value from the modified data structure. Additionally, providing means for generating an estimated cardinality value using the summary statistic value. 
   In a further aspect of the invention there is provided an article comprising, a computer readable signal bearing medium with means stored in the medium for initializing a data structure for representing counts, means stored in the medium for obtaining a data value from a set of data values, and means stored in the medium for transforming the data value into a transformed string. The article further provides means stored in the medium for modifying the data structure with the transformed string, and means stored in the medium for obtaining a summary statistic value from the modified data structure. In addition, the article provides means stored in the medium for generating an estimated cardinality value using the summary statistic value. 
   Other features and advantages of the current invention should be apparent from the following description of embodiments, which illustrates, by way of example, the principles of the invention. 
   DETAILED DESCRIPTION 
   In the performance of database query processing, knowledge of column cardinalities (the number of distinct values in a column) is important for the generation of efficient query plans. The query plans used in query operations directly affects the performance of the relational database management system. 
   The current invention typically enables a database management system to more efficiently compute, when required, a column cardinality estimate without requiring use of all of the column data values. Computation may occur whenever a new data value is inserted into a column or an existing data value is deleted from, or updated in, a column. The invention determines the new estimated column cardinality value using the new data value inserted, deleted or updated. This method of estimation is referred to as “incremental column cardinality maintenance”. The invention incorporates, in a first embodiment, a modified linear counting technique into computing a column cardinality estimate. The invention incorporates, in a second, preferred embodiment, a modified logarithmic counting technique. This technique may be used when computing a column cardinality estimate, to reduce storage requirements of the system catalog table data structure. 
   Referring to  FIG. 1  a data processing system  100  is shown incorporating a database management system  136  containing an embodiment of the present invention. The example shown using a database management system is illustrative of an embodiment of the invention only and does not limit the applicability of the invention that would be appreciated by those of ordinary skill in the art. For example, the invention may be used elsewhere such as with flat files and hierarchical databases and in differently configured data processing systems (simply referred to as computer systems as well). 
   Data processing system  100  comprises central processing unit  120 , memory  122 , videos display  124 , keyboard  126 , pointing device  128 , storage device  130 , (which may be disk or tape or other suitable device for data storage), removable media  144  and network  146 . One of ordinary skill in the art will recognize data processing system  100  as a general purpose digital computer. 
   Relational database management system  136 , as shown, comprises a software module that is stored on and loaded from storage device  130 . While only one system is depicted, it is well known that the data and database management system may be maintained in other embodiments such as combining or connecting different systems by network  146 . Relational database management system  136  comprises functional modules such as query services  132 , cardinality services  134  and logging services  138 . Data items  140  may be rows, columns, tables, associated with and used by, the relational database management system  136 . 
   Data items  140  and RDBMS log data  142  typically include textual data comprised of character strings that may or may not be numeric. Data items  140  and RDBMS log data  142  may also include other uniquely identifiable objects and may be stored on the same storage device  130  or other storage means such as removable media  144 . Cardinality services  134  generates, stores and maintains column cardinality statistics associated with specified data values (data items  140  and RDBMS log data  142 ). Column cardinality statistics generated by cardinality services  134  are then used for query optimization by the query services  132  to build and run query plans. Logging services  138  captures information related to specific database events and records such information in RDBMS log data  142  for subsequent uses such as transaction recovery, reporting or other processing. 
     FIG. 3  illustrates an example of cardinality services  134  of  FIG. 1  used in both embodiments of the invention. Cardinality services  134  ( FIG. 1 ) begins with operation  302  in which the database column is scanned, an initial array of counts is created and initialized to zeros, and an initial column cardinality estimate is obtained. Upon completion of operation  302 , the cardinality services  134  process moves to operation  304 . A database operation request is obtained from the database management system  136  during operation  304 . During operation  305  the next operation is selected depending upon the type of request; INSERT select  306 , DELETE select  308  or UPDATE select  310 . During operation  306 , the column data value is added and the column cardinality estimate is updated. During operation  308 , the column data value would be deleted and the column cardinality estimate updated. During operation  310  the column data value would be updated and the column cardinality estimate would be calculated again as well. 
   After performing any one of the operations  306 ,  308 , or  310 , cardinality services  134  returns to operation  304  to obtain the next database request. It is important to note cardinality services  134  does not revert to operation  302  during which a complete database column scan is performed. In a first embodiment of this invention, a modification of linear counting technique is used to update the cardinality estimate in operations  306 ,  308 , and  310 , and in a preferred embodiment a modification of logarithmic counting technique is used in these operations. Further detail of the process in  FIG. 3  will now be described using  FIGS. 4 , and  5 . 
   Referring to  FIG. 4 , a first embodiment of the present invention extends the linear counting technique to update the cardinality estimate in operations  306 ,  308 , and  310  in  FIG. 3 . Instead of maintaining a bit map, that only indicates the absence or presence of a value, the embodiment extends the system catalog table where column cardinality is stored to include an array of counts associated with each column (see Table  3  of  FIG. 2E ). Using the technique of this invention, an element in the array of counts is either zero, (which indicates no data values hashed to the element), or “N”, (indicating there were “N” data values that hashed to the element position). The array of counts provides a capability to store the result of data value changes. The capability of performing incremental maintenance of column cardinality estimates is then provided through the use of the counts. 
   At an instant in time, the mth entry of the array of counts records the number of data values in a column that have hashed to position m. Column cardinality is then estimated as the number of non-zero entries in the array of counts adjusted for collisions using the same adjustment formula as the simple linear counting mechanism. The number of non-zero entries may be referred to as a summary statistic derived from the array of counts. The unadjusted count may be referred to as the “raw” column cardinality estimate while the adjusted count is referred to as the “final” column cardinality estimate. Handling of INSERT, DELETE, and UPDATE database operations using modified linear counting is described below. 
   In a database INSERT operation, a new value  402  inserted into the set of data values  400 , is hashed by hashing function  404  to a position  408  in array of counts  406 , and the value at position  408  is incremented by one. If the entry was equal to zero prior to being incremented, then the new data value is in fact a new distinct value, the raw column cardinality estimate is incremented by 1 and the final column cardinality is recalculated. If the entry was greater than zero prior to being incremented, then the new value is assumed to be a duplicate of a previous distinct value. In this case both the raw and final column cardinality estimates remain unchanged. 
   In a database DELETE operation, a data value to be deleted from the set of data values  400  is hashed by hashing function  404  to a position  408  in array of counts  406 , and the value at position  408  is decremented by one. Observe that the entry at this position was positive prior to being decremented, since the count at the relative position in the array of counts  406  was previously incremented when this value (or a duplicate of it) was inserted. If the count is zero after being decremented, the raw column cardinality estimate is decremented by one and the final column cardinality is recalculated. Otherwise, the raw and final column cardinality estimates remain unchanged retaining their previous values. 
   A database UPDATE operation can be thought of as deleting the old value followed by inserting the new value. The operations in the delete and insert steps can then be applied sequentially as explained above. 
   For example, consider Table  1 A ( FIG. 2A ), applying the above described operation enabling aspects of the present invention to compute the cardinality of the column called NAME for the first time results in the output shown in the database system catalog table depicted in Table  3  of  FIG. 2E . To keep the example simple, array of counts  406  as illustrated in Table  3  ( FIG. 2E ) contains only  10  elements, but it is understood that it can contain as many elements as desired. Array of counts (0, 2, 0, 1, 1, 0, 0, 0, 0, 0) indicates no data values in column NAME have hashed to positions 1, 3, 6, 7, 8, 9, 10, while two data values from the column hashed to position two. According to Table  1 A ( FIG. 2A ), this value must have been the value “smith”. A single value hashed to positions  4  and  5  in the array of counts  406 . 
   As in the standard linear counting technique, the column cardinality estimate of column NAME, in Table  1 A ( FIG. 2A ), is equal to the number of elements in the array whose content is non-zero. It is easy to see then that there are three elements. Therefore, the column cardinality is set to three (and then adjusted for collisions as before) as shown in the database system catalog of Table  3  ( FIG. 2E ). Assume a new row is added into this table (via an INSERT) to represent an employee with a unique (previously nonexistent) name. To determine the new estimate of column cardinality, cardinality services  134  hashes the new unique value to a position in the array of counts  406  and increments the count at that position by one. In this example, assume the new unique value is “harris” (see Table  2 A of  FIG. 2C ), hashed to position  10  causing array of counts  406  to be (0, 2, 0, 1, 1, 0, 0, 0, 0, 1). The new estimated value of column cardinality is computed by counting the number of non-zero elements in the array of counts  406 . It is easy to see that there are now 4 elements. The database system catalog table is now depicted in Table  4 A of  FIG. 2F . 
   Now assume a previous employee (for example, an entry in column  400  of  FIG. 4 ) is deleted (database DELETE operation). Assume it is the employee “smith” that is deleted from Table  2 A ( FIG. 2C ) causing the table to be now depicted in Table  4 B of  FIG. 2G . Cardinality services  134  hashes the deleted value “smith” to a position in the array of counts  406  and decrements the count at that position by one. Observe that this position must have been position two because “smith” is the only name to occur twice in Table  2 A ( FIG. 2C ). Array of counts  406  is now (0, 1, 0, 1, 1, 0, 0, 0, 0, 1). The new estimated value of the column cardinality is again computed by counting the number of non-zero elements in array of counts  406 . It is easy to see that there are still 4 elements. Column cardinality did not change because the data value deleted was simply a duplicate. The database system catalog table now looks like Table  4 C ( FIG. 2H ). 
   An UPDATE operation can be thought of as a DELETE of the old value followed by an INSERT of the new value. This embodiment of the invention computes a new column cardinality estimate value after an update operation, by sequentially performing the logic for a delete of the old value followed by an insert of the new value. An example of an update is not shown as this is easily understood from the previous insert and delete examples. 
   Referring to  FIG. 5 , a second, preferred embodiment of the present invention extends the logarithmic counting technique to update the cardinality estimate in operations  306 ,  308 , and  310  in  FIG. 4 . As with the first embodiment, the preferred embodiment extends the system catalog table where column cardinality is stored to include an array of counts associated with each column (rather than a bit map as in the standard logarithmic counting technique). Beginning with a set of data values  400  (in  FIG. 4 ), a value such as value  402  is obtained and hashed using a hashing function  404  creating a bit string  502  that is placed into a collection of such strings  500 . Each bit string, such as  502 , is then transformed through transform function  504  retaining the leftmost “1” position in string  502  (and setting all other positions to “0”) to produce a transformed string  506 . Transformed string  506 , viewed as a vector of 0&#39;s and 1&#39;s, is then added to (or subtracted from, as dictated by the associated database operation) the array of counts  508 . The nth position in the array of counts  508 , position  510 , indicates the leftmost “0” position. Position numbers begin at “0” starting at the leftmost element in the array of counts  508 . The relative position number n, (and not the value at that position) is used to calculate the estimated cardinality value using a formula 2n/0.7735. The relative position number n may be referred to as a summary statistic derived from the array of counts. It may also be appreciated that storage of individual bit strings (such as bit string  502 ) into collection  500  may not be required. Individual bit strings (such as bit string  502 ) can be transformed, updating the array of counts  508  on a continuing running count or incremental basis, thereby reducing the storage required. 
   For example, assume “C” (data value  302  of  FIG. 5 ) is hashed to become bit string  502  having a binary value “1101”. String  502  is then transformed into bit string  506  having a binary value “1000” (having a leftmost “1” retained). Value “1000”, viewed as a vector (1,0,0,0), is added to (or subtracted from) the array of counts  508  using simple vector addition (or subtraction), thereby causing the value (count) at exactly one position in the array to be incremented (or decremented). A new cardinality estimate needs to be calculated only if the value of at that one position (such as  510 ) changes (where a change means go to zero, go to one from zero) as a result of the previous addition or subtraction operation. Transformation of the bit string may be implemented more efficiently by simply computing the position m of the leftmost “1” in the initial bit string and then incrementing or decrementing the count in position m of the count array by one. 
   Operation  306  (of  FIG. 3 ) of cardinality services  134  ( FIG. 1 ) is performed to compute the estimate of column cardinality when a new data value has been added to a set of values for which a cardinality estimate is required. During hashing operation  404  (of  FIG. 4 ) a data value  402  is hashed to create a bit string. Upon completion of operation  404 , cardinality services  134  begins operation  504  (of  FIG. 5 ). During operation  504 , the position of the leftmost “1” in the bit string is determined and maintained, all other positions in the bit string being set to zero, creating a transformed bit string. The transformed bit string is added to array of counts  508  (of  FIG. 5 ) causing a counter in position m to be incremented by one. Cardinality services  134  next determines a position n of the leftmost zero entry in the array of counts. If, prior to being incremented, position n, was the leftmost zero entry in array of counts  508 , the column cardinality estimate is updated to a new value. Otherwise, the column cardinality estimate retains its previous value. When required, and using the value n, the new estimated column cardinality value is determined using a formula 2n/q. The process is typically repeated using multiple hash functions (on the order of 64) and the resulting column cardinality estimates averaged to create a final estimate. 
   Operation  308  (of  FIG. 3 ) of cardinality services  134  ( FIG. 1 ) is performed to compute the estimate of column cardinality when a data value has been deleted from the set of data values. During hashing operation  404  (of  FIG. 4 ) the data value being deleted is hashed to create a bit string. The position, m, of the leftmost “1” in the bit string is then determined during operation  504  as before, but the transformed bit string is subtracted from array of counts  508  (of  FIG. 5 ) causing a counter in position m to be decremented by “1”. (Note: the entry in position m is positive prior to being decremented.) Cardinality services  134  next determines a position n of the leftmost zero entry in the array of counts. If, after being decremented, the entry in position m is now the leftmost zero entry in array of counts  508 , then the column cardinality estimate is updated to a new value. Otherwise, the column cardinality estimate retains its previous value. Using the value n, the estimated column cardinality value is determined using a formula 2n/q. The process is typically repeated using multiple hash functions (on the order of 64) and the resulting column cardinality estimates averaged to create a final estimate. 
   It should be reemphasized that although not shown in the diagram one need only compute a new estimate for the column cardinality if the position n of the leftmost “0” in the array of counts has changed after the database operation of INSERT, DELETE or UPDATE. If the value for n has not changed, the previously computed estimate is retained and used as the estimated cardinality value, saving time and resource. 
   As with the extended linear counting technique previously described, the preceding embodiment of the invention extends the logarithmic counting method by replacing the bit map with an array of counts. The array of counts for extended logarithmic counting requires fewer elements than the array required for the extended linear counting method. Because the modified logarithmic counting method reduces the catalog storage requirements, it may be a preferred embodiment. 
   The technique may be better understood using the following examples. First, the array of counts and consequent column-cardinality estimate are computed for the NAME column in the original EMPLOYEE table in Table  1 A ( FIG. 2A ). Then the NAME column is reproduced, along with some associated (hypothetical) hashing information as shown in Table  5 A of  FIG. 2I . 
   In Table  5 A ( FIG. 2I ), the second column is a binary string (bit string) obtained by applying a hash function to the name in the first column. (For simplicity, we assume the hash function produces strings that are 3 bits long; in a real implementation the bit string would be much longer.) Each entry in the third column is obtained by retaining the leftmost 1 in the corresponding binary string in the second column and replacing all of the other bit values by zeroes. The array of counts is then computed by summing the number of 1&#39;s in each column of data in the third column, to yield (3,1,0). 
   Using the array of counts (3,1,0) obtained, the column cardinality is then estimated using 2n/q, (“2” raised to power “n”) where n is the position of the leftmost zero in the array of counts and “q” is a value of 0.7735. In this example, n=2, because counting from the leftmost end, or zero position of the array, it is the second position that has the value of zero (0 position=3, 1st position=1, 2nd position=0). The estimated column cardinality is then 22/0.7735=5.2 
   The process described above may be repeated with “y” different hash functions (typically, y=64) to obtain “y” preliminary estimates, and a final estimate may then be computed by averaging the preliminary estimates. There may then be “y” arrays of counts maintained in the system catalog. It is well known that this technique may be implemented without actually needing y completely different hash functions. For purposes of this example, assume for simplicity that only one hash function is used. Equivalently, this example can be viewed as showing the computations necessary to compute and update a specified preliminary estimate. 
   Continuing the example the last row from the original Table  1 A ( FIG. 2A ) is removed (the entry for smith is deleted) to obtain the example shown in Table  5 B of  FIG. 2J . The array of counts then becomes (2,1,0) and n=2 after a simple vector subtraction, and the column cardinality estimate remains equal to 5.2(n=2 still). 
   By further example, again using the original table in Table  1 A ( FIG. 2A ) and by removing the third row to obtain the result in Table  5 C ( FIG. 2K ), the array of counts now becomes (3,0,0). Since the position of the leftmost 0 in the array is now position  1 , and n=1, the column cardinality estimate is computed to be 21/0.7735=2.6. 
   Similar computations are used when adding a new row to the EMPLOYEE table of Table  1 A ( FIG. 2A ). 
   It is conceivable that one may implement this invention as described in a database management system so that the statistics may be more current with respect to the database activities (that is INSERT, UPDATE and DELETE operations). To reduce the overhead associated with incrementally updating the statistics, a preferred approach may include buffering of INSERT, UPDATE and DELETE operations and then at a later stage generating the incremental statistics based on the buffered values. The invention may be then advantageously used because it does not need to implement a special buffering mechanism to allow incremental statistics update to proceed at a later stage. Buffering may be provided by the logged activity and almost every database system implements logging in some form to allow for recovery in the case where a database has been damaged. Database systems usually store transaction activities into a log file. The technique of this invention can be used in conjunction with the log file information to update the database cardinality statistics in an incremental fashion. 
   When implemented in an automatic manner, the invention may provide current cardinality estimate values at a much lower cost than automating batch-like alternatives since batch versions currently used typically require re-scanning the entire table (or a sample of the table). The invention provides incremental statistics updates while not having to rescan the entire table. The statistics may be incrementally updated during database activities if desired or may be updated at a later stage using the log file approach as described earlier. In both cases re-accessing the base table is not required. Further, a capability of calculating cardinality statistics only when needed may reduce processing requirements. 
   The concepts of the current invention can be further extended to a variety of applications that are clearly within the scope of this invention. Having thus described the current invention with respect to a preferred embodiment as implemented, it will be apparent to those skilled in the art that many modifications and enhancements to the current invention are possible without departing from the basic concepts as described in the preferred embodiment of the current invention. Therefore, what is intended to be protected by way of letters patent should be limited only by the scope of the following claims.