HyperLogLog is an awesome approximation algorithm that addresses the distinct count problem. I am a big fan of HyperLogLog (HLL), so much so that I already wrote about the internals and how HLL solves the distributed distinct count problem. But there’s more to talk about, including HLL with rollup tables.

Rollup Tables and Postgres

Rollup tables are commonly used in Postgres when you don’t need to perform detailed analysis, but you still need to answer basic aggregation queries on older data.

With rollup tables, you can pre-aggregate your older data for the queries you still need to answer. Then you no longer need to store all of the older data, rather, you can delete the older data or roll it off to slower storage—saving space and computing power.

Let’s walk through a rollup table example in Postgres without using HLL.

Rollup tables without HLL—using GitHub events data as an example

For this example we will create a rollup table that aggregates historical data: a GitHub events data set.

Each record in this GitHub data set represents an event created in GitHub, along with key information regarding the event such as event type, creation date, and the user who created the event. (Craig Kerstiens has written about this same data set in the past, in his getting started with GitHub event data on Citus post.)

If you want to create a chart to show the number of GitHub event creations in each minute, a rollup table would be super useful. With a rollup table, you won’t need to store all user events in order to create the chart. Rather, you can aggregate the number of event creations for each minute and just store the aggregated data. You can then throw away the rest of the events data, if you are trying to conserve space.

To illustrate the example above, let’s create github_events table and load data to the table:

CREATE TABLE github_events ( event_id bigint , event_type text , event_public boolean , repo_id bigint , payload jsonb , repo jsonb , user_id bigint , org jsonb , created_at timestamp ); \ COPY github_events FROM events . csv CSV

In this example, I’m assuming you probably won’t perform detailed analysis on your older data on a regular basis. So there is no need to allocate resources for the older data, instead you can use rollup tables and just keep the necessary information in memory. You can create a rollup table for this purpose:

CREATE TABLE github_events_rollup_minute ( created_at timestamp , event_count bigint );

And populate with INSERT/SELECT:

INSERT INTO github_events_rollup_minute ( created_at , event_count ) SELECT date_trunc ( 'minute' , created_at ) AS created_at , COUNT ( * ) AS event_count FROM github_events GROUP BY 1 ;

Now you can store the older (and bigger) data in a less expensive resource like disk so that you can access it in the future—and keep the github_events_rollup_minute table in memory so you can create your analytics dashboard.

By aggregating the data by minute in the example above, you can answer queries like hourly and daily total event creations, but unfortunately it is not possible to know the more granular event creation count for each second.

Further, since you did not keep event creations for each user separately (at least not in this example), you cannot have a separate analysis for each user with this rollup table. All off these are trade-offs.

Without HLL, rollup tables have a few limitations

For queries involving distinct count, rollup tables are less useful. For example, if you pre-aggregate over minutes, you cannot answer queries asking for distinct counts over an hour. You cannot add each minute’s result to have hourly event creations by unique users. Why? Because you are likely to have overlapping records in different minutes.

And if you want to calculate distinct counts constrained by combinations of columns, you would need multiple rollup tables.

Sometimes you want to get event creation count by unique users filtered by date and sometimes you want to get unique event creation counts filtered by event type (and sometimes a combination of both.) With HLL, one rollup table can answer all of these queries—but without HLL, you would need a separate rollup table for each of these different types of queries.

HLL to the rescue

If you do rollups with the HLL data type (instead of rolling up the final unique user count), you can easily overcome the overlapping records problem. HLL encodes the data in a way that allows summing up individual unique counts without re-counting overlapping records.

HLL is also useful if you want to calculate distinct counts constrained by combinations of columns. For example, if you want to get unique event creation counts per date and/or per event type, with HLL, you can use just one rollup table for all combinations.

Whereas without HLL, if you want to calculate distinct counts constrained by combinations of columns, you would need to create:

7 different rollup tables to cover all combinations of 3 columns

15 rollup tables to cover all combinations of 4 columns

2n - 1 rollup tables to cover all combinations in n columns

HLL and rollup tables in action, together

Let’s see how HLL can help us to answer some typical distinct count queries on GitHub events data. If you did not create a github_events table in the previous example, create and populate it now with the GitHub events data set:

CREATE TABLE github_events ( event_id bigint , event_type text , event_public boolean , repo_id bigint , payload jsonb , repo jsonb , user_id bigint , org jsonb , created_at timestamp ); \ COPY github_events FROM events . csv CSV

After creating your table, let’s also create a rollup table. We want to get distinct counts both per user and per event_type basis. Therefore you should use a slightly different rollup table:

DROP TABLE IF EXISTS github_events_rollup_minute ; CREATE TABLE github_events_rollup_minute ( created_at timestamp , event_type text , distinct_user_id_count hll );

Finally, you can use INSERT/SELECT to populate your rollup table and you can use hll_hash_bigint function to hash each user_id . (For an explanation of why you need to hash elements, be sure to read our Citus blog post on distributed counts with HyperLogLog on Postgres):

INSERT INTO github_events_rollup_minute ( created_at , event_type , distinct_user_id_count ) SELECT date_trunc ( 'minute' , created_at ) AS created_at , event_type , sum ( hll_hash_bigint ( user_id )) FROM github_events GROUP BY 1 , 2 ; INSERT 0 2484

What kinds of queries can HLL answer?

Let’s start with a simple case to see how to materialize HLL values to actual distinct counts. To demonstrate that, we will answer the question:

How many distinct users created an event for each event type at each minute at 2016-12-01 05:35:00?

We will just need to use the hll_cardinality function to materialize the HLL data structures to actual distinct count.

SELECT created_at , event_type , hll_cardinality ( distinct_user_id_count ) AS distinct_count FROM github_events_rollup_minute WHERE created_at = '2016-12-01 05:35:00' :: timestamp ORDER BY 2 ; created_at | event_type | distinct_count ---------------------+-------------------------------+------------------ 2016 - 12 - 01 05 : 35 : 00 | CommitCommentEvent | 1 2016 - 12 - 01 05 : 35 : 00 | CreateEvent | 59 2016 - 12 - 01 05 : 35 : 00 | DeleteEvent | 6 2016 - 12 - 01 05 : 35 : 00 | ForkEvent | 20 2016 - 12 - 01 05 : 35 : 00 | GollumEvent | 2 2016 - 12 - 01 05 : 35 : 00 | IssueCommentEvent | 42 2016 - 12 - 01 05 : 35 : 00 | IssuesEvent | 13 2016 - 12 - 01 05 : 35 : 00 | MemberEvent | 4 2016 - 12 - 01 05 : 35 : 00 | PullRequestEvent | 24 2016 - 12 - 01 05 : 35 : 00 | PullRequestReviewCommentEvent | 4 2016 - 12 - 01 05 : 35 : 00 | PushEvent | 254 . 135297564883 2016 - 12 - 01 05 : 35 : 00 | ReleaseEvent | 4 2016 - 12 - 01 05 : 35 : 00 | WatchEvent | 57 ( 13 rows )

Then let’s continue with a query which we could not answer without HLL:

How many distinct users created an event during this one-hour period?

With HLLs, this is easy to answer.

SELECT hll_cardinality ( SUM ( distinct_user_id_count )) AS distinct_count FROM github_events_rollup_minute WHERE created_at BETWEEN '2016-12-01 05:00:00' :: timestamp AND '2016-12-01 06:00:00' :: timestamp ; distinct_count ------------------ 10978 . 2523520687 ( 1 row )

Another question where we can use HLL’s additivity property to answer would be:

How many unique users created an event during each hour at 2016-12-01?

SELECT EXTRACT ( HOUR FROM created_at ) AS hour , hll_cardinality ( SUM ( distinct_user_id_count )) AS distinct_count FROM github_events_rollup_minute WHERE created_at BETWEEN '2016-12-01 00:00:00' :: timestamp AND '2016-12-01 23:59:59' :: timestamp GROUP BY 1 ORDER BY 1 ; hour | distinct_count -------+------------------ 5 | 10598 . 637184899 6 | 17343 . 2846931687 7 | 18182 . 5699816622 8 | 12663 . 9497604266 ( 4 rows )

Since our data is limited, the query only returned 4 rows, but that is not the point of course. Finally, let’s answer a final question:

How many distinct users created a PushEvent during each hour?

SELECT EXTRACT ( HOUR FROM created_at ) AS hour , hll_cardinality ( SUM ( distinct_user_id_count )) AS distinct_push_count FROM github_events_rollup_minute WHERE created_at BETWEEN '2016-12-01 00:00:00' :: timestamp AND '2016-12-01 23:59:59' :: timestamp AND event_type = 'PushEvent' :: text GROUP BY 1 ORDER BY 1 ; hour | distinct_push_count ------+--------------------- 5 | 6206 . 61586498546 6 | 9517 . 80542100396 7 | 10370 . 4087640166 8 | 7067 . 26073810357 ( 4 rows )

A rollup table with HLL is worth a thousand rollup tables without HLL

Yes, I believe a rollup table with HLL is worth a thousand rollup tables without HLL.

Well, maybe not a thousand, but it is true that one rollup table with HLL can answer lots of queries where otherwise you would need a different rollup table for each query. Above, we demonstrated that with HLL, 4 example queries all can be answered with a single rollup table— and without HLL, we would have needed 3 separate rollup tables to answer all these queries.

In the real world, if you do not take advantage of HLL you are likely to need even more rollup tables to support your analytics queries. Basically for all combinations of n constraints, you would need 2n - 1 rollup tables whereas with HLL just one rollup table can do the job.

One rollup table (with HLL) is obviously much easier to maintain than multiple rollup tables. And that one rollup table uses significantly less memory too. In some cases, without HLL, the overhead of using rollup tables can become too expensive and exceeds the benefit of using rollup tables, so people decide not to use rollup tables at all.

Want to learn more about HLL in Postgres?

HLL is not only useful to create rollup tables, HLL is useful in distributed systems, too. Just as with rollup tables, in a distributed system, such as Citus, we often place different parts of our data in different nodes, hence we are likely to have overlapping records at different nodes. Thus, the clever techniques HLL uses to encode data to merge separate unique counts (and address the overlapping record problem) can also help in distributed systems.

If you want to learn more about HLL, read how HLL can be used in distributed systems, where we explained the internals of HLL and how HLL merges separate unique counts without counting overlapping records.

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