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Cardinality Estimation Benchmark

This benchmark consolidates the code and workloads from two papers: Flow Loss: learning cardinality estimates that matter and Robust Qery Driven Cardinality Estimation under Changing Workloads. Please cite the Flow-Loss paper for introducing the CEB benchmark; it does not explore other workloads as much, and the focus is on describing and implementing the new loss function (Flow-Loss). The robust-cardinalities paper focuses on improved featurizations with a focus on training on different workloads, and develops particular techniques for improving robustness. In general, both approaches can be used together, but the approaches in the robust-cardinalities paper are much easier to implement and describe. For a further discussion about the differences between these approaches, check out the Related Works section in the robust-cardinalities paper, and a direct comparison of the experiments in an online appendix.




Our goal is to use multiple database / query workloads to evaluate learned models for estimation accuracy, and performance on downstream query optimization tasks. We use a custom networkx based format for representing the query data (see Query Format for details). This is because CEB contains ground truth data, and bitmap features, for millions of SQLs (query + all its subplans), and storing everything in plain-text is very inefficient.

IMDb Workloads

We'll suggest to start with around 3000 representative queries from the 16 IMDb CEB templates with:

There have been several query workloads released on IMDb over the years. Download all the cardinalities, and featurization bitmap information for JOB,CEB, and JOBLight-train with:

bash scripts/

This downloads all the queries to queries/<workload>. It also downloads sample bitmaps and join bitmaps (used for featurizing queries) to queries/allbitmaps/<workload>. Note: there are two versions of the IMDb-CEB workload: the full version, ceb-imdb-full with ~13K queries, and a smaller subset, with ~3K queries, ceb-imdb. In most experiments, the 3k queries version seems good enough to use.

Ergast CEB

StackExchange CEB

bash scripts/


Standalone training / evaluation notebooks. These should be convenient to get started, but using the script, as described in Learned Models is more flexible for running experiments.

Also, for PostgreSQL based evaluation (e.g., for plan costs or runtimes, you will need to setup PostgreSQL as described in PostgreSQL.)

pip3 install jupyter

And then go to any of the notebooks in Notebooks/ and execute the cells in order.


Optional For some of the plan graph visualizations, we will need graphviz. Note: This is not neccessary to run the benchmark, and can be hard to install with some system configurations. You can usually install it with:

sudo apt-get install graphviz

If you want to use captum for visualizing neural net feature importance attributions

pip3 install captum

Flow-Loss FlowLoss implementation is done in C for efficiency reasons; On Linux machines, do:

cd flow_loss_cpp && make

This isn't required if you aren't using flow-loss training runs.



We use docker to install and configure PostgreSQL, and setup the relevant databases. Make sure that you have Docker installed appropriately for your system, with the docker daemon running. PostgreSQL requires a username, which we copy from an environement variable $LCARD_USER while setting it up in docker. Similarly, set $LCARD_PORT to the local port you want to use to connect to the PostgreSQL instance running in docker. Here are the commands to set it up:

cd docker
export LCARD_USER=ceb
export LCARD_PORT=5432
sudo docker build --build-arg LCARD_USER=${LCARD_USER} -t pg12 .
sudo docker run -itd --shm-size=1g --name card-db -p ${LCARD_PORT}:5432 -d pg12
sudo docker restart card-db
sudo docker exec -it card-db /

Note: Depending on the settings of your docker instance, you may not require sudo in the above commands. Also, in the docker run command, you may want to choose the --shm-size parameter depending on your requirements.

Optionally you can use the following command to install the stackexchange database; But the stackexchange database is A LOT larger than the IMDb database --- make sure you have up to 150GB space on your device before running the following command.

sudo docker exec -it card-db /

# These commands ensure there are only foreign key : primary key
# indexes on the stackexchange database; Without the drop_indexes.sql command,
#the database contains a few indexes that utilize multiple columns, which may
#potentially be better suited for the join topology in the stackexchange
#database, but which index setup is the most appropriate remains to be explored further.

psql -d stack -U $LCARD_USER -p $LCARD_PORT -h localhost < drop_indexes.sql
psql -d stack -U $LCARD_USER -p $LCARD_PORT -h localhost < create_indexes.sql

The StackExchange database was based on one of the dumps released from the StackExchange foundation; We've used various heuristics / simplifications in constructing the database from the StackExchange dump, and restore the database from a PostgreSQL snapshot (see for its download link). The StackExchange database holds a lot of potential to develop more challenging query templates as well, although we have not explored it as much as IMDb. Refer to the workload section for a comparison between IMDb and StackExchange workloads.

Here are a few useful commands to check / debug your setup:

# if your instance gets restarted / docker image gets shutdown
sudo docker restart card-db

# get a bash shell within the docker image
sudo docker exec -it card-db bash
# note that postgresql data on docker is stored at /var/lib/postgresql/data

# connect psql on your host to the postgresql server running on docker
psql -d imdb -h localhost -U imdb -p $LCARD_PORT

To clean up everything, if you don't want to use the docker image anymore, run:



Follow instructions provided here. After setting up the database, you should be able to use the scripts here by passing in the appropriate user, db_name, db_host, and ports to appropriate python function calls.

Python Requirements

These can be installed with

pip3 install -r requirements.txt

To test the whole setup, including the docker installation, run

python3 tests/

Running Experiments

We provide several config files that set up the different experiments in directiory configs/. Running the experiment would look like:

python3 --config configs/config-custom.yaml

Several of the losses (Q-Error, Relative-PostgresPlanCost) on different workloads are printed after every epoch. Please see the papers for the definition of PostgresPlanCost ---- this is a proxy for runtimes, and can be computed efficiently if you have PostgreSQL setup as described in setup. Clear differences in plan costs are often reflected in clear runtime differences as well --- see getting runtimes section.

Here are some interesting parameters in the config files to control these:

  • model:eval_epoch: N # computes losses every N epochs.
  • eval:use_wandb: 0/1` # if 1, uses wandb to log results.

Next, lets briefly describe each of the config files and the key fields.

  • config-joblight.yaml ---> default MSCN setup; trained on joblight, and evaluated on JOB or CEB.

  • config-joblight-robust.yaml ---> Robust-MSCN setup; trained on joblight, and evaluated on JOB or CEB. The differences compared to default MSCN is parameters:

    • featurizer:job\_bitmap : 1 # uses join bitmap
    • featurizer:sample\_bitmap : 0 # doesn't use sample bitmap
    • model: onehot\_dropout : 1 # uses the query masking
    • model: onehot\_mask\_truep : 0.8 # prob used for not masking features

For instance, running the two files above with:

python3 --config configs/config-joblight.yaml
python3 --config configs/config-joblight-robust.yaml

And comparing the numbers for 'PostgresPlanCost-C-Relative-JOB' would show the kind of benefits we can get using our techniues. And, in general, you can use these files as templates and change the following directories to use a different train / test setup. For e.g., the following would train on queries from CEB, and test on all of JOB. * data:query\_dir: "./queries/ceb" * data:eval\_query\_dir: "./queries/job/"

  • config-custom.yaml and config-custom-robust.yaml: similar to the config files above, these specify a small, self-contained experiment with just two templates that show the key ideas with the query masking approach. These are results mentioned in A.2 in our appendix .

  • config-flowloss.yaml --> compared to previous files, we change loss\_fn\_name to flowloss. In general, the flowloss loss function can be used with any of the experiments before. In the Flow-Loss paper, we ran the key experiments with:

    • data:train_test_split_kind : "template"
    • data:diff_templates_seed: 1 # in the paper, seeds=1-10 for 10 experiments

More details

Query Format

First, let us explore the basic properties of the queries that we store:

from query_representation.query import *

qfn = "queries/imdb/4a/4a100.pkl"
qrep = load_qrep(qfn)

# extract basic properties of the query representation format

print("""Query has {} tables, {} joins, {} subplans.""".format(
    len(qrep["join_graph"].nodes()), len(qrep["join_graph"].edges()),

tables, aliases = get_tables(qrep)

print("Tables: ")
for i,table in enumerate(tables):
    print(table, aliases[i])

print("Joins: ")
joins = get_joins(qrep)

preds, pred_cols, pred_types, pred_vals = get_predicates(qrep)
print("Predicates: ")
for i in range(len(preds)):
    for j, pred in enumerate(preds[i]):
        print(pred.strip(" "))
        print("     Predicate column: ", pred_cols[i][j])
        print("       Predicate type: ", pred_types[i][j])
        print("     Predicate values: ", pred_vals[i][j])

Next, we see how to access each of the subplans, and their cardinality estimates.

from query_representation.query import *

qfn = "queries/imdb/4a/4a100.pkl"
qrep = load_qrep(qfn)

# for getting cardinality estimates of every subplan in the query
ests = get_postgres_cardinalities(qrep)
trues = get_true_cardinalities(qrep)

for k,v in ests.items():
    print("Subplan, joining tables: ", k)
    subsql = subplan_to_sql(qrep, k)
    print("Subplan SQL: ", subsql)
    print("   True cardinality: ", trues[k])
    print("PostgreSQL estimate: ", v)

Please look at the implementations in query_representation/ for seeing how the information is represented, and how to directly manipulate the internal fields of the qrep object.

A few other points to note:

  • all queries uses table aliases in the workload (e.g., TITLE as t). A lot of the helper methods for generating cardinalities etc. assume this, so if you want to use these tools to generate data for new queries, use aliases.

Evaluating estimates

Given a query, and estimates for each of its subplans, we can use various error functions to evaluate how good the estimates are. We can directly compare the true values and the estimated values, using for instance:

  • Q-Error, Relative Error, Absolute Error etc. Q-Error is generally considered to be the most useful of these metrics from the perspective of query-optimization.

Alternatively, we can compare how good was the plan generated by using the estimated values. This will depend on the query optimizer - in particular the properties of the cost model we choose, and the search function etc. We provide implementations for the two options as discussed in the paper, but by changing configurations of the PostgreSQL cost model, or adding more complex custom cost models, there can be many possibilities considered here.

  • Postgres Plan Cost (PPC): this uses the PostgreSQL cost model with two restrictions --- no materialization and parallelism. For experimenting with different configurations, check the function set_cost_model in losses/ and add additional configurations.

  • Plan-Cost: this considers only left deep plans, and uses a simple user specified cost function (referred to as C in the paper).

Here is a self contained example showing the API to compute these different kind of errors on a single query.

from os.path import dirname, join, realpath
import query_representation
from query_representation.query import *
from evaluation.eval_fns import *
from psycopg2 import OperationalError

qfn = join(dirname(realpath(query_representation.__path__._path[0])), "queries/imdb/4a/4a100.pkl")
qrep = load_qrep(qfn)
ests = get_postgres_cardinalities(qrep)

# estimation errors for each subplan in the query
qerr_fn = get_eval_fn("qerr")
abs_fn = get_eval_fn("abs")
rel_fn = get_eval_fn("rel")

qerr = qerr_fn.eval([qrep], [ests], result_dir=None)
abs_err = abs_fn.eval([qrep], [ests], result_dir=None)
relerr = rel_fn.eval([qrep], [ests],result_dir=None)

print("avg q-error: {}, avg abs-error: {}, avg relative error: {}".format(
              np.round(np.mean(qerr),2), np.round(np.mean(abs_err), 2),
                            np.round(np.mean(relerr), 2)))

# check the function comments to see the description of the arguments
# can change the db arguments appropriately depending on the PostgreSQL
# installation.
ppc = get_eval_fn("ppc")
port = 5432
    ppc = ppc.eval([qrep], [ests], user="ceb", pwd="password", db_name="imdb",
            db_host="localhost", port=port, num_processes=-1, result_dir=None,
except OperationalError:
    print(f"PGSQL not running at port {port}")

# we considered only one query, so the returned lists have just one element
print("PPC is: {}".format(np.round(ppc[0])))

pc = get_eval_fn("plancost")
plan_cost = pc.eval([qrep], [ests], cost_model="C")
print("Plan-Cost is: {}".format(np.round(plan_cost[0])))

For evaluating either true cardinalities, or PostgreSQL estimates on all queries in CEB / or just from some templates, run:

python3 --query_templates 1a,2a --algs true,postgres --eval_fns qerr,ppc,plancost --query_dir queries/imdb

Similarly, if you have setup JOB, JOB-M in the previous steps, you can run:

python3 --query_templates 1a,2a --algs true,postgres --eval_fns qerr,ppc,plancost --query_dir queries/job
python3 --query_templates 1a,2a --algs true,postgres --eval_fns qerr,ppc,plancost --query_dir queries/jobm

Since, JOB (and JOB-M), have only 2-4 queries per template, we do not separate them out by templates.

If you have setup the StackExchange DB and workload, then you can run a similar command, but passing the additional required parameters for the db_name:

python3 --query_templates all --algs true,postgres --eval_fns qerr,ppc,plancost --query_dir queries/stack --db_name stack

Notes on Postgres Plan Cost

  • What is a good cost? This is very context dependent; What we really care about is runtimes, but plan costs are nice proxies for them because they can be computed quickly, and repeatedly. But these costs don't have units. But, it can be helpful to compare them with the Postgres Plan Cost generated using the true cardinality as estimators (use flag: --algs true).

  • We can normalize these Postgres Plan Costs by dividing by the optimal cost OR subtracting the optimal cost; But it is not clear what is the best approach; For instance, it is common to see that some templates in CEB (e.g., 3a,4a), have much lower magnitude of PPC (e.g., < 100k), while some templates have PPC in the order of > 1e7; For a particular query, if the optimal cost is 20k, and your estimator's cost is 40k, then this would lead to a relative error of 2.0; While for a large query, with an optimal cost of 1e7, and the estimator's cost of 1.5e7, would lead to a relative error of 1.5. But in these cases, as expected, we find the runtime differences to be more prominent in the latter case.

Adding other DBMS backends

We can similarly define MySQL Plan Cost, and plan costs using other database backends. Plan costs are computed using the following steps:

  1. Insert cardinality estimates into the optimizer; Get the output plan. (Note that since we used the estimated cardinalities, the cost we get for this plan does not mean much).
  2. Insert the true cardinality estimates into the optimizer; Cost the plan from the previous step using the true cardinalities. This reflects how good that plan is in reality; we call it the DBMS Plan Cost.

These require two abilities: inserting cardinality estimates into an optimizer (typically, not provided by most optimizers), and then precisely specifiying a plan (for the step 2 above); It is usually possible to precisely specify a plan, although this can be tricky. An example of this process with PostgreSQL is in the file evaluation/; look at the function _get_pg_plancosts;

We've a mysql fork that implements these requirements; But it is somewhat hacky and not easy to use. We plan to eventually add a cleaner version to this repo. Similarly, you can add other database backends as well.

Getting runtimes

There are two steps to generating the runtimes; first, we generate the Postgres Plan Cost, and the corresponding SQLs to execute. These SQL strings would be annotated with various pg_hint_plan hints to enforce join order, operator selection and index Postgres Plan Costselection (see losses/ for details). These strings can be executed on PostgreSQL with pg_hint_plan loaded, but you may want to use a different setup for execution --- so other processes on the computer do not interfere with the execution times, and do things like clear the cache after every execution (cold start), or repeat each execution a few times etc. depending on your goals. Here, we provide a simple example to execute the SQLs, but note that this does not clear caches, or take care about isolating the execution from other processes, so these timings won't be reliable.

# writes out the file results/Postgres/PostgresPlanCost.csv with the sqls to execute
# the sqls are modified with pg_hint_plan hints to use the cardinalities output
# by the given algorithm' estimates;
python3 --algs postgres -n 5 --query_template 1a --eval_fns qerr,ppc,plancost

# executes the sqls on PostgreSQL server, with the given credientials
python3 evaluation/ --port 5432 --user ceb --pwd password --result_dir results/Postgres

In the Flow-Loss paper, we executed these plans on AWS machines w/ NVME hard disks, using the code in this repo. It is not clear what is the best environment to evaluate runtime of these plans, and you should choose the appropriate settings for your project.

Visualizing Results

When you execute,

python3 --algs postgres -n 5 --query_template 1a --eval_fns qerr,ppc

it should create files results/Postgres/train_query_plans.pdf etc. which contain a pdf with the query plan generated using the cardinalities from PostgreSQL, and additional details.

For instance, consider the query 11c in the Join Order Benchmark. The query plan based on PostgreSQL estimates is 4-5x worse than the query plan based on the true cardinalities; We can clearly see why the PostgreSQL estimates mess up by looking at the accompanying visualization plot

Note that the cardinalities are rounded to the nearest thousand. The red node is the most expensive cost node; PostgreSQL was estimating a very low cardinality (blue), and went for a nested loop join. The true cardinality (orange), is larger, and a Hash Join was probably a better choice (if you check the same plan with flag --algs true , you will see that the best plan does use a similar plan, but with Hash Join in the third join).

Learned Models


We provide baseline implementation of a few common learning algorithms. Here are a few sample commands to run these:

python3 --query_templates 1a,2a --algs xgb --eval_fns qerr,ppc,plancost --result_dir results
python3 --query_templates 1a,2a --algs mscn --eval_fns qerr,ppc,plancost --result_dir results --lr 0.0001
python3 --query_templates all --algs fcnn --eval_fns qerr,ppc,plancost --result_dir results --lr 0.0001

Please look at cardinality_estimation/ for the list of provided implementations.

Train Test Split

We suggest two ways to split the dataset; --train_test_split_kind query splits train/test samples among the queries on each template. So for instance, if we run the following

python3 --query_templates all --algs fcnn --eval_fns qerr,ppc,plancost --result_dir results --train_test_split_kind query --val_size 0.2 --test_size 0.5

the, for each template, we will select 0.2% queries in the validation set, and divide the remaining equally into train and test sets.

A more challenging scenario will be to have a few unseen templates. For this, use the flag --train_test_split_kind template. For example:

python3 --query_templates all --algs fcnn --eval_fns qerr,ppc,plancost --result_dir results --train_test_split_kind template --test_size 0.5 --diff_templates_seed 1

This will divide the templates equally into train / test sets; Note: we can have a validation set in this case as well, but since the templates performance' can be very different from each other, its not clear if the validation set helps much. Since there are relatively few templates, the exact split can create very different experiments, thus, in this scenario we suggest cross validating across multiple such splits (e.g., by using --diff_templates_seed 1, --diff_templates_seed 2, etc.).

Flattened 1d v/s Set features

The featurization scheme is implemented in cardinality_estimation/ Look at the keyword arguments for Featurizer.setup() for the various configurations we use to generate the 1-d featurization of the queries.

The goal is to featurize each subplan in a query, so we can make cardinality predictions on them; There are two featurization approaches.

Flattened This flattens a given subplan into a single 1d feature vector. This can be very convenient as most learning methods operate on 1d arrays; As a drawback, it requires reserving a spot in this feature vector for each column used in the workloads; Thus, you need to know the exact workloads the query will be evaluated on (this is not uncommon, as templated / dashboard queries would match such workloads, but it does reduce the scope of such classifiers.

Set This maps a given subplan into three sets (table, predicate, joins) of feature vectors; For instance, the tables set will contain one feature vector for each of the tables in the subplan, and the predicate set will contain one feature vector for each of the predicate filters in the subplan. If a subplan has three tables, five filter predicates, and two joins, it will map the subplan into a (3,TABLE_FEATURE_SIZE), (5, PREDICATE_FEATURE_SIZE), (2, JOIN_FEATURE_SIZE) vectors. Notice, for e.g., with predicates, the featurizer only needs to map a filter predicate on a single column to a feature vector; This is used in the set based MSCN architecture, which learns on pooled aggregations of different sized sets like these. The main benefit is that it avoids potentially massively large flattened 1d feature vectors, and can support a larger class of ad-hoc queries. The drawback is that different subplans have different number of tables, predicates etc. And in order to get the MSCN implemenations working, we need to pad these with zeros so all `sets' are of same size, thus it requires A LOT of additional memory spent on just padding small subplans, e.g., a subplan which has 1 predicate filter will have size (1,PREDICATE_FEATURE_SIZE). But to pass it to the MSCN architecture, we'll need to pad it with zeros so its size will be (MAX_PREDICATE_FILTERS, PREDICATE_FEATURE_SIZE), where the MAX_PREDICATE_FILTERS is the largest value it is in the batch we pass into the MSCN model. We have not explored optimizing / using sparse representations for the MSCN architecture, which can perhaps save these memory cost blowups.

Using the flag --load_padded_mscn_feats 0 will only load the non-zero sets, and pad them as needed. The current implementation is very slow, and it is almost 10x slower to train like this (we can use parallel dataloaders, or implement this step in C etc. to speed this up considerably). --load_padded_mscn_feats 1 will pre-load all these padded sets into memory (very unpractical on the full CEB workload), but runs fast.

Featurization Knobs

There are several assumptions that go into the featurization step, and a lot of scope for improvement. I'll describe the most interesting ones here:

  • PostgreSQL estimates We find that these estimates significantly improve model performance (although they do slow inference times in a practical system, as the featurization will require calling the PostgreSQL estimator; the impact of this slowdown needs to be studied)

  • Featurizing Categorical Columns : It's easy to featurize continuous columns; What about =, or IN predicates? Its unclear what is the best approach in general. Providing heuristic estimates, like PostgreSQL estimates, is a general approach, but might not be as useful. Sample Bitmaps is another approach that can be quite informative for the model, but these are large 1d vectors, which significantly increase the size of feature vectors / memory requirements etc.; We take the approach of hashing the predicate filter values to a small array, whose size is controlled by the feature: --max_discrete_featurizing_buckets; Intuitively, if the number of unique values in the column is not too much larger than the number of buckets we use, then this can be a useful signal for workloads with repeating patterns; In CEB, we typically had (IN, =) predicates on columns with not very large alphabet sizes, so --max_discrete_featurizing_buckets 10 significantly improves the performance of these models;

But its debatable if this is scalable to more challenging workloads. Thus, in general, it may be interesting to develop methods, and evaluate models, while setting --max_discrete_featurizing_buckets 1; In a previous paper, Cost Guided Cardinality Estimation, we used this setting. Methods that can improve model performance when max_discrete_featurizing_buckets == 1, might perhaps model a more common scenario where the alphabet size of categorical columns is too large, so these features become less useful.

Loss Functions

The standard approach is to optimize the neural networks for Q-Error; One way to implement this is to first take the log of the target values by (use flag: --ynormalization log), and then optimize for mean squared error. As shown in the paper, this is close enough to optimizing for Q-Error, and has some nicer properties (smoother function than Q-Error, which may help in training). In practice, we find this to work slightly better in general than optimizing for q-error directly.

Generating Queries

Queries in CEB are generated based on templates. Example templates are in the directory /templates/. More details about the templating scheme, including the base SQL structure of the templates in the IMDb workload are given here templates. For generating queries from such a template, you can use:

python3 query_gen/ --query_output_dir qreps --template_dir ./templates/imdb/3a/ -n 10 --user ceb --pwd password --db_name imdb --port 5432

Generating Cardinalities

Here, we will provide an example that shows how to go from a bunch of sql files to the qrep objects which contain all the cardinality estimates for subplans, and is the format used to represent queries in this project. As a simple example, we have added the JOB-light queries in the repo; these have small join graphs, thus, the cardinalities can be generated very fast.

# Change the input / output directories appropriately in the script etc.
python3 scripts/

# this updates all the subplans of each qrep object with the postgresql
# estimates that we use in featurization etc. of the subplans. This is stored in
# the field \[subplan\]\["cardinality"\]\["expected"\]
python3 scripts/ --port 5432 --db_name imdb --query_dir queries/joblight/all_joblight/ --card_type pg --key_name expected --pwd password --user ceb

# this updates all the subplans of each qrep object with the actual
# estimates that we use in featurization etc. of the subplans. This is stored in
# the field \[subplan\]\["cardinality"\]\["actual"\]
# This step could take really long depending on the size of the query, the
# evaluation setup you have etc. Also, be careful with the resource utilization
#by this script: by default, it parallelizes the executions, but this might
#cause PostgreSQL to crash in case there is not enough resources (check flags
#    --no\_parallel 1 to do it one query at a time)
python3 scripts/ --port 5432 --db_name imdb --query_dir queries/joblight/all_joblight/ --card_type actual --key_name actual --pwd password --user ceb

## TODO: generate bitmaps for these

TODO: Using wanderjoin

Future Work


Cardinality Estimation Benchmark







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