Query optimizer

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The query optimizer is the component of a database management system that attempts to determine the most efficient way to execute a query. The optimizer considers the possible query plans for a given input query, and attempts to determine which of those plans will be the most efficient. Cost-based query optimizers assign an estimated "cost" to each possible query plan, and choose the plan with the smallest cost. Costs are used to estimate the runtime cost of evaluating the query, in terms of the number of I/O operations required, the CPU requirements, and other factors determined from the data dictionary. The set of query plans examined is formed by examining the possible access paths (e.g. index scan, sequential scan) and join algorithms (e.g. sort-merge join, hash join, nested loops). The search space can become quite large depending on the complexity of the SQL query.

Generally, the query optimizer cannot be accessed directly by users: once queries are submitted to database server, and parsed by the parser, they are then passed to the query optimizer where optimization occurs. However, some database engines allow guiding the query optimizer with hints.


[edit] Implementation

Most query optimizers represent query plans as a tree of "plan nodes". A plan node encapsulates a single operation that is required to execute the query. The nodes are arranged as a tree, in which intermediate results flow from the bottom of the tree to the top. Each node has zero or more child nodes -- those are nodes whose output is fed as input to the parent node. For example, a join node will have two child nodes, which represent the two join operands, whereas a sort node would have a single child node (the input to be sorted). The leaves of the tree are nodes which produce results by scanning the disk, for example by performing an index scan or a sequential scan.

[edit] Join ordering

The performance of a query plan is determined largely by the order in which the tables are joined. For example, when joining 3 tables A, B, C of size 10 rows, 10,000 rows, and 1,000,000 rows, respectively, a query plan that joins B and C first can take several orders-of-magnitude more time to execute than one that joins A and C first. Most query optimizers determine join order via a dynamic programming algorithm pioneered by IBM's System R database project. This algorithm works in two stages:

  1. First, all ways to access each relation in the query are computed. Every relation in the query can be accessed via a sequential scan. If there is an index on a relation that can be used to answer a predicate in the query, an index scan can also be used. For each relation, the optimizer records the cheapest way to scan the relation, as well as the cheapest way to scan the relation that produces records in a particular sorted order.
  2. The optimizer then considers combining each pair of relations for which a join condition exists. For each pair, the optimizer will consider the available join algorithms implemented by the DBMS. It will preserve the cheapest way to join each pair of relations, in addition to the cheapest way to join each pair of relations that produces its output according to a particular sort order.
  3. Then all three-relation query plans are computed, by joining each two-relation plan produced by the previous phase with the remaining relations in the query.

In this manner, a query plan is eventually produced that joins all the queries in the relation. Note that the algorithm keeps track of the sort order of the result set produced by a query plan, also called an interesting order. During dynamic programming, one query plan is considered to beat another query plan that produces the same result, only if they produce the same sort order. This is done for two reasons. First, a particular sort order can avoid a redundant sort operation later on in processing the query. Second, a particular sort order can speed up a subsequent join because it clusters the data in a particular way.

Historically, System-R derived query optimizers would often only consider left-deep query plans, which first join two base tables together, then join the intermediate result with another base table, and so on. This heuristic reduces the number of plans that need to be considered (n! instead of 4^n), but may result in not considering the optimal query plan. This heuristic is drawn from the observation that join algorithms such as nested loops only require a single tuple (aka row) of the outer relation at a time. Therefore, a left-deep query plan means that fewer tuples need to be held in memory at any time: the outer relation's join plan need only be executed until a single tuple is produced, and then the inner base relation can be scanned (this technique is called "pipelining").

Subsequent query optimizers have expanded this plan space to consider "bushy" query plans, where both operands to a join operator could be intermediate results from other joins. Such bushy plans are especially important in parallel computers because they allow different portions of the plan to be evaluated independently.

[edit] Query planning for nested SQL queries

A SQL query to a modern relational DBMS does more than just selections and joins. In particular, SQL queries often nest several layers of SPJ blocks (Select-Project-Join) , by means of group by, exists, and not exists operators. In some cases such nested SQL queries can be flattened into a select-project-join query, but not always. Query plans for nested SQL queries can also be chosen using the same dynamic programming algorithm as used for join ordering, but this can lead to an enormous escalation in query optimization time. So some database management systems use an alternative rule-based approach that uses a query graph model.

[edit] Cost estimation

One of the hardest problems in query optimization is to accurately estimate the costs of alternative query plans. Optimizers cost query plans using a mathematical model of query execution costs that relies heavily on estimates of the cardinality, or number of tuples, flowing through each edge in a query plan. Cardinality estimation in turn depends on estimates of the selection factor of predicates in the query. Traditionally, database systems estimate selectivities through fairly detailed statistics on the distribution of values in each column, such as histograms. This technique works well for estimation of selectivities of individual predicates. However many queries have conjunctions of predicates such as select count(*) from R where R.make='Honda' and R.model='Accord'. Query predicates are often highly correlated (for example, model='Accord' implies make='Honda'), and it is very hard to estimate the selectivity of the conjunct in general. Poor cardinality estimates and uncaught correlation are one of the main reasons why query optimizers pick poor query plans. This is one reason why a DBA should regularly update the database statistics, especially after major data loads/unloads.

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