Cardinality Estimation

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Cardinality estimation is a classic problem. Pinot solves it with multiple ways each of which has a trade-off between accuracy and latency.
Accurate Results
Functions:
DistinctCount(x) -> LONG
Returns accurate count for all unique values in a column.
The underlying implementation is using a IntOpenHashSet in library: it.unimi.dsi:fastutil:8.2.3 to hold all the unique values.
Approximation Results
It usually takes a lot of resources and time to compute accurate results for unique counting on large datasets. In some circumstances, we can tolerate a certain error rate, in which case we can use approximation functions to tackle this problem.
HyperLogLog
​HyperLogLog is an approximation algorithm for unique counting. It uses fixed number of bits to estimate the cardinality of given data set.
Pinot leverages HyperLogLog Class in library com.clearspring.analytics:stream:2.7.0as the data structure to hold intermediate results.
Functions:
DistinctCountHLL(x)_ -> LONG_
For column type INT/LONG/FLOAT/DOUBLE/STRING , Pinot treats each value as an individual entry to add into HyperLogLog Object, then compute the approximation by calling method cardinality().
For column type BYTES, Pinot treats each value as a serialized HyperLogLog Object with pre-aggregated values inside. The bytes value is generated by org.apache.pinot.core.common.ObjectSerDeUtils.HYPER_LOG_LOG_SER_DE.serialize(hyperLogLog).
All deserialized HyperLogLog object will be merged into one then calling method **cardinality() **to get the approximated unique count.
Theta Sketches
The Theta Sketch framework enables set operations over a stream of data, and can also be used for cardinality estimation. Pinot leverages the Sketch Class and its extensions from the library org.apache.datasketches:datasketches-java:1.2.0-incubating to perform distinct counting as well as evaluating set operations.
Functions:
DistinctCountThetaSketch(<thetaSketchColumn>, <thetaSketchParams>, predicate1, predicate2..., postAggregationExpressionToEvaluate**) **-> LONG
thetaSketchColumn (required): Name of the column to aggregate on.
thetaSketchParams (required): Parameters for constructing the intermediate theta-sketches. Currently, the only supported parameter is nominalEntries.
predicates (optional)_: _ These are individual predicates of form lhs <op> rhs which are applied on rows selected by the where clause. During intermediate sketch aggregation, sketches from the thetaSketchColumn that satisfies these predicates are unionized individually. For example, all filtered rows that match country=USA are unionized into a single sketch. Complex predicates that are created by combining (AND/OR) of individual predicates is supported.
postAggregationExpressionToEvaluate (required): The set operation to perform on the individual intermediate sketches for each of the predicates. Currently supported operations are SET_DIFF, SET_UNION, SET_INTERSECT , where DIFF requires two arguments and the UNION/INTERSECT allow more than two arguments.
In the example query below, the where clause is responsible for identifying the matching rows. Note, the where clause can be completely independent of the postAggregationExpression. Once matching rows are identified, each server unionizes all the sketches that match the individual predicates, i.e. country='USA' , device='mobile' in this case. Once the broker receives the intermediate sketches for each of these individual predicates from all servers, it performs the final aggregation by evaluating the postAggregationExpression and returns the final cardinality of the resulting sketch.
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select distinctCountThetaSketch(
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  sketchCol, 
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  'nominalEntries=1024', 
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  'country'=''USA'' AND 'state'=''CA'', 'device'=''mobile'', 'SET_INTERSECT($1, $2)'
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) 
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from table 
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where country = 'USA' or device = 'mobile...' 
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DistinctCountRawThetaSketch(<thetaSketchColumn>, <thetaSketchParams>, predicate1, predicate2..., postAggregationExpressionToEvaluate**)** -> HexEncoded Serialized Sketch Bytes
This is the same as the previous function, except it returns the byte serialized sketch instead of the cardinality sketch. Since Pinot returns responses as JSON strings, bytes are returned as hex encoded strings. The hex encoded string can be deserialized into sketch by using the library org.apache.commons.codec.binaryas Hex.decodeHex(stringValue.toCharArray()).
User-Defined Functions (UDFs)
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Contents
Accurate Results
Approximation Results
HyperLogLog
Theta Sketches