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Derby Optimizer Design

This document describes the Derby Optimizer. This is a work-in-progress derived from Javadoc comments and from explanations Jeffrey Lichtman and others posted to the Derby lists. Please post questions, comments, and corrections to derby-dev@db.apache.org.


Jeffrey Lichtman wrote the original implementation of the optimizer. What follows below is a description of the optimizer he posted to the Derby mailing list.

The optimizer currently only considers left-deep trees. That is, when looking at joins, it doesn't consider join nodes to the right of other join nodes - the join trees it considers are skewed to the left. I thought this would be a good first implementation of the optimizer. Bushy trees (where the join tree can take any shape) are harder to implement but are often useful for big multi-way decision-support joins.

During optimization the join order is represented as an array of Optimizables. The first element in the array is the leftmost table in the join tree, and the successive elements in the array are the joining tables in the left-deep tree.

The optimizer does an exhaustive search of query plans, going through all the join orders and, for each join order, all of the access paths for that order. It remembers the cheapest complete plan it has found so far, and does cost-based search space pruning. That is, it doesn't consider plans that are more expensive that the best plan found so far.

The optimizer goes through the search space depth-first. In other words, it adds a table to the join order, then goes through all the access paths for that table (choosing the cheapest one) before going on to the next position in the join order. When it gets all the way to the end of the join order, with all of the tables accounted for, it considers whether the plan it is looking at is the best one found so far. If so, it remembers it. Eventually, it exhausts all the tables to consider at a given depth in the join order, and it has to back up to the previous position in the join order and consider the next table there.

Every time the optimizer adds a table to the prospective join order, it figures out which parts of the WHERE clause can be evaluated at that position in the order and pushes these expressions down to that position so they can be used there. For example, if you have a five-way join of tables t1, t2, t3, t4 and t5, and the current permutation being considered is t3 - t1 - t2 (with t3 as the outermost table and t2 as the innermost), it can evaluate the join "t3.c1 = t2.c2" at the third position in the join order, so when it adds table t2 it pushes the expression down to that level in the order. Later, when it removes t2 from the join order to consider some other table there, it pulls the expression back out of the join order.

getNextPermutation() does the adding (and deletion) of tables to the join order under consideration by the optimizer. getNextDecoratedPermutation() goes through all the access paths for the current permutation (in the current implementation, it only has to consider the access paths for the innermost table in the join order, as the search is done depth-first). You can think of a decorated permutation as a join order with things like indexes and join strategies "decorating" the nodes.

The Optimizable interface represents anything in the query that can have an access path. In practice an Optimizable is usually a base table, but it can be anything that appears in a FROM list (for example, standard SQL allows a UNION in the FROM list). Different Optimizables have different choices for access paths. The optimizer uses the nextAccessPath() method on Optimizable to step through the different access paths. These include different join strategies (such as nested loop and hash join) and different conglomerates (the base table and the different indexes). Sometimes the Optimizable has to decide whether a given access path is feasible (for example, hash join is only feasible for equijoins).

I'm leaving out a whole lot of details, like how the optimizer does costing for sort avoidance and how it handles join order dependencies (e.g. when an "exists" or "in" subquery is flattened to an existence join, the join order musn't be inverted under the current implementation).

Example of a 5-way Join

The optimizer looks at so many potential plans in a five-way join that it's not feasible to show all of them in an manually-written explanation.

Let's take the following query:

select *
from t1, t2, t3, t4, t5
where t1.c1 = t2.c2
and    t1.c3 = t3.c4
and    t3.c5 = t4.c6
and    t4.c7 = t5.c8
and    t1.c9 = 1
and    t3.c10 = 2
and    t5.c11 = 3          

One possible way to execute this query is to take the tables in the order of the FROM clause. For each row in a table, join it with the matching rows from the next table to form a set of joined row. The plan would look something like this (I hope the formatting doesn't get screwed up):

             /      \
          JOIN    t5
           /      \
        JOIN    t4
        /     \
    JOIN    t3
   /       \
t1       t2

This is a left-deep tree. That is. it's skewed to the left. Let's assume for the sake of argument that each JOIN node is a nested-loop join. What this means is that each JOIN node gets a row from its left (outer) table and probes into its right (inner) table to find all the matching rows. For all but the leftmost JOIN node, the outer table is also a JOIN. So, at execution, this plan goes all the way down to the left, gets the first qualifying row from t1, then finds a matching row in t2. It then puts the matching rows from t1 and t2 together into a joined row and feeds it up to the JOIN node above it. This JOIN node uses its outer row to probe into t3 to find a matching row. When it finds such a row, it puts together its outer and inner rows into a joined row, which it feeds to the JOIN node above it. It keeps doing this all the way up the plan. When the top JOIN node finds a matching row in t5, it returns that row from the SELECT statement.

More sophisticated optimizers consider "bushy" trees, which can take shapes other than the left-deep shape shown above. For example, it might consider a plan with the following join tree:

         /       \
   JOIN       JOIN
   /     \      /      \
t1    t2    t3    JOIN
                     /     \
                    t4    t5

As you can see, the tables are in the same order but the shape of the join tree is entirely different. As I mentioned in my original mail, bushy trees are harder to implement but they are good for some types of big decision-support queries.

Because the Derby optimizer only models left-deep trees, it doesn't have to model the shape of the tree. All it has to model is the order of the tables in the tree (since the tree is always the same shape for a given number of tables). It does this the simple way: by using an array representing the assignment of tables to positions in the join order.

The basic idea of a cost-based optimizer is to come up with an estimated cost for all the possible execution plans for a query and to choose the cheapest plan. The number of possible plans grows with the number of tables, indexes, join strategies, etc. Most optimizers do something to reduce the search space, so that for big queries the best plan (or a reasonable plan) is found in an acceptable length of time. One way the Derby optimizer prunes its search space is by skipping over plans that it knows will be more expensive than the best plan it's found so far.

The optimizer does this by depth-first searching. That is, rather than coming up with a join order for all the tables in the query and then considering all the access paths for those tables, it adds one table at a time to the join order and figures out the best access path for that table (in its current spot in the join order) before going on to add another table to the join order. While doing this, it keeps track of the cost of the plan its considering so far. If, when it adds a table to the join order, it finds that this makes the current plan under consideration more costly than the best plan found so far, it abandons the consideration of that table in that position of the join order. By doing this, the optimizer can avoid considering many join orders. This is important when there are a lot of tables in the query, because the number of join orders is the factorial of the number of tables.

For example, let's say that in the sample query given above, the optimizer has already found a complete plan with an estimated cost of 10000. Now suppose it is considering the following partial join order:

(outer) t4 - t5 (inner)

Let's say this partial plan has an estimated cost of 2000. Now suppose the optimizer considers placing the table t1 as the next table in the join order:

(outer) t4 - t5 - t2 (inner)

Note that the query has no direct join clause between t1 and either t4 or t5. The optimizer would go through all possible access paths for t2 in this context, and would see that with no useful qualification on the table it would have to do a full scan of t2 for every outer row resulting from the join of t4 and t5. If t2 is anything but a very small table, it could be expensive. Let's say the estimated total best cost for t2 in this position in the join order is 50000. That would make the total cost of the query equal to 52000, which is higher than the cost of the best plan found so far (10000). So it doesn't make sense to look at this join order any further. Rather than consider the following join orders:

(outer) t4 - t5 - t2 - t1 - t3 (inner)

(outer) t4 - t5 - t2 - t3 - t1 (inner)

the optimizer abandons consideration of any plan starting with t4 - t5 - t2.

Potential Improvements to the Optimizer

It's hard to consider the optimizer by itself. Many optimizer enhancements would work with changes in other areas, especially execution.

One area that I think needs work is hash joins. The current implementation uses an in-memory hash table. The optimizer avoids using the hash join strategy when it estimates that the hash table would use too much memory. There are a few problems with this: the optimizer doesn't really know how much memory is available, its estimates of memory usage are crude and possibly inaccurate, and it's possible for the query to fail if a hash table gets too big during execution.

I would like to see hash tables that spill to disk. Ideally, the hash table should be an in-memory structure with a conglomerate as a backing store. I would want the backing store to be used only when necessary - that is, only when the hash table grows too big. The biggest problem with this idea is how to estimate the cost of building and maintaining the table. One approach could be to put a limit on the number of in-memory rows in the hash table and use a statistical formula for the cost of reading a row, using the number of in-memory rows versus the total number of rows to estimate the chances of finding a row in memory.

Another approach could be to use weak references in managing the hash table (a weak reference is a Java construct that allows the garbage collector to nominate an object for garbage collection even when it has a reference to it). Weak references are useful for memory caches that adjust themselves to the memory available to the JVM. One of our original ideas for Derby (nee Cloudscape) is that it should be a low-maintenance DBMS, with little intervention required to keep a working system running. A self-managing cache could help with this - it would adjust itself to environments with different amounts of memory (although small-memory environments could hurt performance). I don't know how the optimizer would estimate the cost for building and maintaining a hash table in this case.

I also think merge joins are worth considering, especially if nothing is done about hash joins. Merge joins are useful for many of the same types of queries as hash joins and, since they use the sorter (assuming the joined rows are not already ordered on the join colums) they can work even for large tables (because the sorter spills to disk if the data being sorted won't fit in memory). Merge joins can have a very low cost if the rows are already ordered (which they can be if there are indexes on the join columns). Merge joins can also work well with sort avoidance if the ordering for the merge is the same as for the ORDER BY clause.

Switching gears, another problem is the cost of user-defined functions. What do you do with a query like this?:

select *
from t1, t2, t3
where t1.c1 = user_defined_function(t2.c2)
and t2.c3 = t3.c4

If the user-defined function is cheap and there's an index on t1.c1, you may want to call the function for every row in t2 and use the result to probe into the index on t1. On the other hand, if the function is expensive, you may want to try to execute it as few times as possible, which could make it unfeasible to use it to probe into t1. Currently Derby has no modeling for the cost of user-defined functions and avoids pushing them down into the query plan (that is, it calculates user-defined functions as late as possible before returning the rows from the query).

This may seem trivial, but keep in mind that a user-defined function can do anything, from something as simple as returning a constant to as complex as executing a query on another DBMS. It really can be important to know the cost of a user-defined function.

One possible approach would be to have a way of telling the DBMS to execute the function and remember how long it takes, and then store this in a system catalog for the optimizer to use. Another approach would be to allow the user to register the cost of a function as low, medium or high.

Switching gears again, another feature I think would be generically useful would be indexes on expressions (instead of just on columns). One potential use for this feature is case-independent searches (which can be done now, but which tend to be slow because the functions involved prevent the optimizer from using an index). The biggest problem here is the representation of index definitions in the SYSCONGLOMERATES system table (which assumes that an index column corresponds to a column in a base table).

Another area for investigation is the flattening of subqueries to joins. Currently, the language compiler flattens IN and EXISTS subqueries to types of joins. This is good because it gives the optimizer more options in choosing query plans for these types of subqueries, and it also allows the optimizer to get better cost estimates (for complex technical reasons I won't go into here). There are other types of subqueries that could be flattened - for example, a NOT IN or NOT EXISTS subquery can often be flattened to an outer join.

Another thing that could be done is to allow the optimizer to invert the join order of IN and EXISTS subqueries. As mentioned above, these subqueries are often flattened to joins. The joins are special, in that at execution it looks for only one match in the inner table per row from the outer table. This strategy requires that the table in the IN or EXISTS subquery remain inner to the joining table from outside the subquery. It would be possible to invert the join order if a sort were done on the subquery table to eliminate duplicate joining values. (Actually, I'm oversimplifying here, but I would have to write a treatise otherwise.)