6.830 Lab 4: Query Optimization

Assigned: Wednesday, April 10, 2013
Due: Monday, April 29, 2013

Version History:

In this lab, you will implement a query optimizer on top of SimpleDB. The main tasks include implementing a selectivity estimation framework and a cost-based optimizer. You have freedom as to exactly what you implement, but we recommend using something similar to the Selinger cost-based optimizer discussed in class (see these slides from a previous offering of the course).

The remainder of this document describes what is involved in adding optimizer support and provides a basic outline of how you might add this support to your database.

As with the previous lab, we recommend that you start as early as possible.

1. Getting started

You should begin with the code you submitted for Lab 3. (If you did not submit code for Lab 3, or your solution didn't work properly, contact us to discuss options.)

We have provided you with extra test cases as well as source code files for this lab that are not in the original code distribution you received. We reiterate that the unit tests we provide are to help guide your implementation along, but they are not intended to be comprehensive or to establish correctness. You will need to add these new test cases to your release. The easiest way to do this is to untar the new code in the same directory as your top-level simpledb directory, as follows:

1.1. Implementation hints

We suggest exercises along this document to guide your implementation, but you may find that a different order makes more sense for you. As before, we will grade your assignment by looking at your code and verifying that you have passed the test for the ant targets test and systemtest. See Section 3.4 for a complete discussion of grading and the tests you will need to pass.

Here's a rough outline of one way you might proceed with this lab. More details on these steps are given in Section 2 below.

2. Optimizer outline

Recall that the main idea of a cost-based optimizer is to: In this lab, you will implement code to perform both of these functions.

The optimizer will be invoked from simpledb/Parser.java. You may wish to review the lab 2 parser exercise before starting this lab. Briefly, if you have a catalog file catalog.txt describing your tables, you can run the parser by typing:

java -jar dist/simpledb.jar parser catalog.txt

When the Parser is invoked, it will compute statistics over all of the tables (using statistics code you provide). When a query is issued, the parser will convert the query into a logical plan representation and then call your query optimizer to generate an optimal plan.

2.1 Overall Optimizer Structure

Before getting started with the implementation, you need to understand the overall structure of the SimpleDB optimizer.

The overall control flow of the SimpleDB modules of the parser and optimizer is shown in Figure 1.

Figure 1: Diagram illustrating classes, methods, and objects used in the parser and optimizer.

The key at the bottom explains the symbols; you will implement the components with double-borders. The classes and methods will be explained in more detail in the text that follows (you may wish to refer back to this diagram), but the basic operation is as follows:

  1. Parser.java constructs a set of table statistics (stored in the statsMap container) when it is initialized. It then waits for a query to be input, and calls the method parseQuery on that query.
  2. parseQuery first constructs a LogicalPlan that represents the parsed query. parseQuery then calls the method physicalPlan on the LogicalPlan instance it has constructed. The physicalPlan method returns a DBIterator object that can be used to actually run the query.

In the exercises to come, you will implement the methods that help physicalPlan devise an optimal plan.

2.2. Statistics Estimation

Accurately estimating plan cost is quite tricky. In this lab, we will focus only on the cost of sequences of joins and base table accesses. We won't worry about access method selection (since we only have one access method, table scans) or the costs of additional operators (like aggregates). You are only required to consider left-deep plans for this lab. See Section 2.3 for a description of additional "bonus" optimizer features you might implement, including an approach for handling bushy plans.

2.2.1 Overall Plan Cost

We will write join plans of the form p=t1 join t2 join ... tn , which signifies a left deep join where t1 is the left-most join (deepest in the tree). Given a plan like p, its cost can be expressed as:
scancost(t1) + scancost(t2) + joincost(t1 join t2) +
scancost(t3) + joincost((t1 join t2) join t3) +
Here, scancost(t1) is the I/O cost of scanning table t1, joincost(t1,t2) is the CPU cost to join t1 to t2. To make I/O and CPU cost comparable, typically a constant scaling factor is used, e.g.:
cost(predicate application) = 1
cost(pageScan) = SCALING_FACTOR x cost(predicate application)
For this lab, you can ignore the effects of caching (e.g., assume that every access to a table incurs the full cost of a scan) -- again, this is something you may add as an optional bonus extension to your lab in Section 2.3. Therefore, scancost(t1) is simply the number of pages in t1 x SCALING_FACTOR.

2.2.2 Join Cost

When using nested loops joins, recall that the cost of a join between two tables t1 and t2 (where t1 is the outer) is simply:
joincost(t1 join t2) = scancost(t1) + ntups(t1) x scancost(t2) //IO cost
                       + ntups(t1) x ntups(t2)  //CPU cost
Here, ntups(t1) is the number of tuples in table t1.

2.2.3 Filter Selectivity

ntups can be directly computed for a base table by scanning that table. Estimating ntups for a table with one or more selection predicates over it can be trickier -- this is the filter selectivity estimation problem. Here's one approach that you might use, based on computing a histogram over the values in the table:

Figure 2: Diagram illustrating the histograms you will implement in Lab 4.

In the next two exercises, you will code to perform selectivity estimation of joins and filters.

Exercise 1: IntHistogram.java

You will need to implement some way to record table statistics for selectivity estimation. We have provided a skeleton class, IntHistogram that will do this. Our intent is that you calculate histograms using the bucket-based method described above, but you are free to use some other method so long as it provides reasonable selectivity estimates.

We have provided a class StringHistogram that uses IntHistogram to compute selecitivites for String predicates. You may modify StringHistogram if you want to implement a better estimator, though you should not need to in order to complete this lab.

After completing this exercise, you should be able to pass the IntHistogramTest unit test (you are not required to pass this test if you choose not to implement histogram-based selectivity estimation).


Exercise 2: TableStats.java

The class TableStats contains methods that compute the number of tuples and pages in a table and that estimate the selectivity of predicates over the fields of that table. The query parser we have created creates one instance of TableStats per table, and passes these structures into your query optimizer (which you will need in later exercises).

You should fill in the following methods and classes in TableStats:

You may wish to modify the constructor of TableStats.java to, for example, compute histograms over the fields as described above for purposes of selectivity estimation.

After completing these tasks you should be able to pass the unit tests in TableStatsTest.

2.2.4 Join Cardinality

Finally, observe that the cost for the join plan p above includes expressions of the form joincost((t1 join t2) join t3). To evaluate this expression, you need some way to estimate the size (ntups) of t1 join t2. This join cardinality estimation problem is harder than the filter selectivity estimation problem. In this lab, you aren't required to do anything fancy for this, though one of the optional excercises in Section 2.4 includes a histogram-based method for join selectivity estimation.

While implementing, your simple solution, you should keep in mind the following:

Exercise 3: Join Cost Estimation

The class JoinOptimizer.java includes all of the methods for ordering and computing costs of joins. In this exercise, you will write the methods for estimating the selectivity and cost of a join, specifically:

After implementing these methods, you should be able to pass the unit tests in JoinOptimizerTest.java, other than orderJoinsTest.

2.3 Join Ordering

Now that you have implemented methods for estimating costs, you will implement the Selinger optimizer. For these methods, joins are expressed as a list of join nodes (e.g., predicates over two tables) as opposed to a list of relations to join as described in class.

Translating the algorithm given in these slides to the join node list form mentioned above, an outline in pseudocode would be:

1. j = set of join nodes
2. for (i in 1...|j|):
3.     for s in {all length i subsets of j}
4.       bestPlan = {}
5.       for s' in {all length d-1 subsets of s}
6.            subplan = optjoin(s')
7.            plan = best way to join (s-s') to subplan
8.            if (cost(plan) < cost(bestPlan))
9.               bestPlan = plan
10.      optjoin(s) = bestPlan
11. return optjoin(j)
To help you implement this algorithm, we have provided several classes and methods to assist you. First, the method enumerateSubsets(Vector v, int size) in JoinOptimizer.java will return a set of all of the subsets of v of size size. This method is not particularly efficient; you can earn extra credit by implementing a more efficient enumerator.

Second, we have provided the method:

    private CostCard computeCostAndCardOfSubplan(HashMap<String, TableStats> stats, 
                                                HashMap<String, Double> filterSelectivities, 
                                                LogicalJoinNode joinToRemove,  
                                                Set<LogicalJoinNode> joinSet,
                                                double bestCostSoFar,
                                                PlanCache pc) 
Given a subset of joins (joinSet), and a join to remove from this set (joinToRemove), this method computes the best way to join joinToRemove to joinSet - {joinToRemove}. It returns this best method in a CostCard object, which includes the cost, cardinality, and best join ordering (as a vector). computeCostAndCardOfSubplan may return null, if no plan can be found (because, for example, there is no left-deep join that is possible), or if the cost of all plans is greater than the bestCostSoFar argument. The method uses a cache of previous joins called pc (optjoin in the psuedocode above) to quickly lookup the fastest way to join joinSet - {joinToRemove}. The other arguments (stats and filterSelectivities) are passed into the orderJoins method that you must implement as a part of Exercise 4, and are explained below. This method essentially performs lines 6--8 of the psuedocode described earlier.

Third, we have provided the method:

    private void printJoins(Vector<LogicalJoinNode> js, 
                           PlanCache pc,
                           HashMap<String, TableStats> stats,
                           HashMap<String, Double> selectivities)
This method can be used to display a graphical representation of a join plan (when the "explain" flag is set via the "-explain" option to the optimizer, for example).

Fourth, we have provided a class PlanCache that can be used to cache the best way to join a subset of the joins considered so far in your implementation of Selinger (an instance of this class is needed to use computeCostAndCardOfSubplan).


Exercise 4: Join Ordering

In JoinOptimizer.java, implement the method:

  Vector orderJoins(HashMap<String, TableStats> stats, 
                   HashMap<String, Double> filterSelectivities,  
                   boolean explain)
This method should operate on the joins class member, returning a new Vector that specifies the order in which joins should be done. Item 0 of this vector indicates the left-most, bottom-most join in a left-deep plan. Adjacent joins in the returned vector should share at least one field to ensure the plan is left-deep. Here stats is an object that lets you find the TableStats for a given table name that appears in the FROM list of the query. filterSelectivities allows you to find the selectivity of any predicates over a table; it is guaranteed to have one entry per table name in the FROM list. Finally, explain specifies that you should output a representation of the join order for informational purposes.

You may wish to use the helper methods and classes described above to assist in your implementation. Roughly, your implementation should follow the psuedocode above, looping through subset sizes, subsets, and sub-plans of subsets, calling computeCostAndCardOfSubplan and building a PlanCache object that stores the minimal-cost way to perform each subset join.

After implementing this method, you should be able to pass the test OrderJoinsTest. You should also pass the system test QueryTest.

2.4 Extra Credit

In this section, we describe several optional excercises that you may implement for extra credit. These are less well defined than the previous exercises but give you a chance to show off your mastery of query optimization!

Bonus Exercises. Each of these bonuses is worth up to 5% extra credit:

You have now completed this lab. Good work!

3. Logistics

You must submit your code (see below) as well as a short (2 pages, maximum) writeup describing your approach. This writeup should:

3.1. Collaboration

This lab should be manageable for a single person, but if you prefer to work with a partner, this is also OK. Larger groups are not allowed. Please indicate clearly who you worked with, if anyone, on your writeup.

3.2. Submitting your assignment

To submit your code, please create a 6.830-lab4.tar.gz tarball (such that, untarred, it creates a 6.830-lab4 directory with your source code at 6.830-lab4/src/simpledb). Include your individual writeup in the tarball you submit on Stellar:

$ cp lab4_writeup.pdf 6.830-lab4

$ tar -cvzf 6.830-lab4.tar.gz 6.830-lab4
Please do not use the ant handin target to create your submission archive.

Submit your tarball for the Lab 4 assigment on Stellar (Stellar Site Homework Section). You may submit your code multiple times; we will use the latest version you submit that arrives before the deadline (before 11:59pm on the due date). If applicable, please indicate your partner in your writeup. Please submit your writeup as a PDF or plain text file only (no .rtf/.doc/.docx/.odf formats please).

3.3. Submitting a bug

SimpleDB is a relatively complex piece of code. It is very possible you are going to find bugs, inconsistencies, and bad, outdated, or incorrect documentation, etc.

We ask you, therefore, to do this lab with an adventurous mindset. Don't get mad if something is not clear, or even wrong; rather, try to figure it out yourself or send us a friendly email. Please submit (friendly!) bug reports to 6830-staff@nms.csail.mit.edu. When you do, please try to include:

You can also post on the class page on Piazza if you feel you have run into a bug.

3.4 Grading

50% of your grade will be based on whether or not your code passes the test suite we will run over it. These tests will be a superset of the tests we have provided. Before handing in your code, you should make sure it produces no errors (passes all of the tests) from both ant test and ant systemtest.

Important: before testing, we will replace your build.xml, HeapFileEncoder.java, and the entire contents of the test/ directory with our version of these files! This means you cannot change the format of .dat files! You should therefore be careful changing our APIs. This also means you need to test whether your code compiles with our test programs. In other words, we will untar your tarball, replace the files mentioned above, compile it, and then grade it. It will look roughly like this:

$ gunzip 6.830-lab4.tar.gz
$ tar xvf 6.830-lab4.tar
$ cd 6.830-lab4
[replace build.xml, HeapFileEncoder.java, and test]
$ ant test
$ ant systemtest
[additional tests]
If any of these commands fail, we'll be unhappy, and, therefore, so will your grade.

An additional 50% of your grade will be based on the quality of your writeup and our subjective evaluation of your code.

We've had a lot of fun designing this assignment, and we hope you enjoy hacking on it!