"Volatile data about the database, stored in the system catalog so that the optimizer has access to it." (Peter Gulutzan & Trudy Pelzer, "SQL Performance Tuning", 2002)
"Information about tables and indexes stored in the data dictionary used to assist the cost-based optimizer when deciding how to run a given query." (Bob Bryla, "Oracle Database Foundations", 2004)
"SQL Server keeps statistics about the distribution of the key values in each index and uses these statistics to determine what index(es) to use in query processing." (Thomas Moore, "EXAM CRAM™ 2: Designing and Implementing Databases with SQL Server 2000 Enterprise Edition", 2005)
"Information about the distribution of the key values in each index and uses these statistics to determine what index(es) to use in query processing." (Thomas Moore, "MCTS 70-431: Implementing and Maintaining Microsoft SQL Server 2005", 2006)
"Statistics are a small sample of a whole used to represent the whole. In SQL Server, statistics are maintained on indexes and used by the query optimizer to determine which indexes to use for a given query. Instead of scanning an entire index (the entire population), statistical data (a sampling) is maintained on the index." (Darril Gibson, "MCITP SQL Server 2005 Database Developer All-in-One Exam Guide", 2008)
[database statistics:] "In query optimization, refers to measurements about database objects, such as the number of rows in a table, number of disk blocks used, maximum and average row length, number of columns in each row, number of distinct values in each column, etc. Such statistics give a snapshot of database characteristics." (Carlos Coronel et al, "Database Systems: Design, Implementation, and Management" 9th Ed., 2011)
[optimizer statistics:] "Details about the database its object used by the optimizer to select the best execution plan for each SQL statement. Categories include table statistics such as numbers of rows, index statistics such as B-tree levels, system statistics such as CPU and I/O performance, and column statistics such as number of nulls." (Oracle, "Database SQL Tuning Guide Glossary", 2013)
[column statistics:] "Statistics about columns that the optimizer uses to determine optimal execution plans. Column statistics include the number of distinct column values, low value, high value, and number of nulls." (Oracle, "Database SQL Tuning Guide Glossary", 2013)
[index statistics:] "Statistics about indexes that the optimizer uses to determine whether to perform a full table scan or an index scan. Index statistics include B-tree levels, leaf block counts, the index clustering factor, distinct keys, and number of rows in the index." (Oracle, "Database SQL Tuning Guide Glossary", 2013)
"Statistics about tables that the optimizer uses to determine table access cost, join cardinality, join order, and so on. Table statistics include row counts, block counts, empty blocks, average free space per block, number of chained rows, average row length, and staleness of the statistics on the table." (Oracle, "Database SQL Tuning Guide Glossary", 2013)
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