Less than ideal cardinality estimates lead to suboptimal query plans. To address this issue, this paper proposed a tighter bound for intermediate join cardinalities based on the concept of hypergraph.

1. Pessimistic Cardinality Estimation:
Presented by Zhuomin Liu

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Introduction & Background
● How to define a join order.
○ Binary join reorder algorithm. ------ need a good count estimation model.
○ Intermediate join count estimation. ------ need a precise cardinality calculation.
○ Cardinality for a join plan. ------ how to estimate it?
○ Naive solution:
!"#$ %&'(#$&)#*+ = max()12* 31+ %&'(#$&)#*+, '#5ℎ* 31+ %&'(#$&)#*+)
● What results are cardinality underestimation caused?
○ The count of join are overestimated.
○ Choose a very slow join order.

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Introduction & Background
● What does paper do?
○ An approach to tightening join cardinality upper bounds.
○ A method of generating entropic bounding formulas.
○ A partition budgeting strategy to control space and time complexity.
○ Demonstrate approach in multiple datasets.
● Pre-knowledge: hypergraph

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Introduction & Background

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Approach
● The Bound Sketch
○ !(#) — a relation with attributes #
○ % — a random hash function & ↦ 1, … , +
○ + — domain of hash function 1, … , +
○ , — an array of hash values, , ∈ + #
○ ,[/] — hash value of attribute /
○ !1
— subset of relational instance !, as those tuples 2 ∈ ! that hash to ,
!1
= 2 ∈ !: % 2 / = , / , ∀/ ∈ #
678 = !1
978 / = :;<
{>∈?:@ > A1[;]}
|{2: 2 / = D}|

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Approach
● The Bound Sketch example
Relation !(#, %)
Hash function ℎ(#) = #%2

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Approach
● Cardinality Bounds example
○ ! ", $, % : ' ", $ , ( $, % , ) %, "
○ random variables *, +, , for ", $, %
○ joint entropy ℎ(", $, %) = log(|!(", $, %)|)

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Approach
● Cardinality Bounds example
|"($)| ≤
'()*
+
, '*)-
.
, '-)(
/
'()-
/
, '*)(
+
, '-)*
.
('()
0
1('*)
0
1('-)
0
1
|"($)| ≤ 2
3∈ 5 6
789
'(:)*:
+
, '*:)-:
.
, '-:)(:
/
'(:)-:
/
, '*:)(:
+
, '-:)*:
.
('(:)
0
1('*:)
0
1('-:)
0
1

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Approach
● Selection Propagation and Processing

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Approach
● How to decide Hash Partition Budgeting
○ fixed size for each attribute?
○ let sum size of attributes fixed?
● Hash Partition Budgeting
○ fixed max size ! for each attribute.
○ distribute to attributes covered unconditionally by a relation.

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Approach
● Bound Formula Generation
○ enumerate all relation cover set in hypergraph
○ for each relation in a set, calculate its contribution for formula
● Example

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Evaluation
● Progressive Bound Tightness
○ 45 GooglePlus community edge-sets
○ Postgres 9.6.6 instance
○ non-cryptographic Murmur3 algorithm

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Evaluation
● Plan Execution Time Improvement

14. Thank You !