Fundamental Propertjes of the GraphQL Language Olaf Hartjg - - PowerPoint PPT Presentation

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Fundamental Propertjes of the GraphQL Language Olaf Hartjg - - PowerPoint PPT Presentation

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Fundamental Propertjes of the GraphQL Language Olaf Hartjg @olafiartjg Joint work with Jorge Prez from the Universidad de Chile Olaf Hartjg Fundamental Propertjes of the GraphQL Language 2 Olaf Hartjg Fundamental Propertjes of the

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Fundamental Propertjes of the GraphQL Language

Olaf Hartjg

@olafiartjg

Joint work with Jorge Pérez from the Universidad de Chile

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2 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

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3 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

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4 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Why study the GraphQL language formally?

Highlight intrinsic limitations

  • f all possible implementations

Identify optimization opportunities Clarify possible corner cases

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5 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Our Results in a Nutshell

Formal definition of the language Study of computational complexity (the language admits really efficient evaluation methods) Solution to the problem of large results

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Formalizatjon of GraphQL

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7 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Why?

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8 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Why?

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9 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Why?

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10 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

GraphQL Graphs (Our Formalizatjon)

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11 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

GraphQL Graphs (Our Formalizatjon)

Typed nodes

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12 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

GraphQL Graphs (Our Formalizatjon)

Typed nodes One special node

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13 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

GraphQL Graphs (Our Formalizatjon)

Typed nodes One special node Node properties

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14 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

GraphQL Graphs (Our Formalizatjon)

Typed nodes One special node Node properties Edge properties

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15 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

GraphQL Graphs (Our Formalizatjon)

Typed nodes One special node Node properties Edge properties

We also formalize the notions of GraphQL schema and schema satisfaction based on this data model

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16 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Formalizatjon of Query Evaluatjon Functjon

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17 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Formalizatjon of Query Evaluatjon Functjon

⟦

friends { name }⟧

u

=

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18 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Formalizatjon of Query Evaluatjon Functjon

= friends: [ ]

⟦

friends { name }⟧

u

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19 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Formalizatjon of Query Evaluatjon Functjon

friends: [ { ⟦ name⟧

v} { ⟦

name⟧

w} ]

=

⟦

friends { name }⟧

u

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20 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Formalizatjon of Query Evaluatjon Functjon

= friends: [ {name:R2-D2} {name:Han} ]

⟦

friends { name }⟧

u

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21 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Formalizatjon of Query Evaluatjon Functjon

⟦

⟧ hero[episode:EMPIRE] { friends {name} }

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22 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Formalizatjon of Query Evaluatjon Functjon

⟦

⟧

r

hero[episode:EMPIRE] { friends {name} }

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23 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Formalizatjon of Query Evaluatjon Functjon

⟦

⟧

r

hero[episode:EMPIRE] { friends {name} }

= hero: { ⟦ friends {name} ⟧

u }

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24 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Formalizatjon of Query Evaluatjon Functjon

⟦

⟧

r

hero[episode:EMPIRE] { friends {name} }

= hero: { ⟦ friends {name} ⟧

u }

= hero: { friends: [ {name:R2-D2} {name:Han} ] }

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Complexity Analysis

Evaluation Problem

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26 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Evaluatjon Problem of GraphQL

GraphQL query q GraphQL graph G data value d yes no Does d occur in the result of q over G? Does d occur in the result of q over G?

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27 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Complexity Classes

PSPACE NP P

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28 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Complexity of Evaluatjon Problems

PSPACE NP P Relational Algebra SPARQL Conjunctive Queries BGPs (SPARQL)

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29 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Complexity of Evaluatjon Problems

PSPACE NP P NL GraphQL Relational Algebra SPARQL Conjunctive Queries BGPs (SPARQL)

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Complexity Analysis

Enumeration Problem

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31 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Non-Redundancy

hero { name: Luke friends: [ { name: R2-D2} { name: Han} ] id: 1000 name: Luke friends: [ { id: 2001} { id: 1002} ] } hero[episode: EMPIRE] { name friends { name } id name friends { id } }

Valid query Invalid result

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32 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Non-Redundancy

hero[episode: EMPIRE] { name friends { name } id name friends { id } }

Valid query

hero { name: Luke friends: [ { name: R2-D2 Id: 2001 } { name: Han Id: 1002 } ] id: 1000 }

Fields are collected before answering Correct result

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33 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Non-Redundancy

hero { name: Luke friends: [ { name: R2-D2 Id: 2001 } { name: Han Id: 1002 } ] id: 1000 } hero[episode: EMPIRE] { name friends { name id } id }

Fields are collected before answering Non-redundant query Correct result

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34 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Another Complicatjon: Type Restrictjons

hero[episode: EMPIRE] { name friends {

  • n Droid { name }
  • n Human { id }

name } }

Valid query Invalid result

hero { name: Luke friends: [ { name: R2-D2 name: R2-D2 } { id: 1002 name: Han } ] }

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35 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Another Complicatjon: Type Restrictjons

hero[episode: EMPIRE] { name friends {

  • n Droid { name }
  • n Human { id }

name } }

Valid query Correct result

hero { name: Luke friends: [ { name: R2-D2 } { id: 1002 name: Han } ] }

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36 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Another Complicatjon: Type Restrictjons

hero[episode: EMPIRE] { name friends {

  • n Droid { name }
  • n Human { id name }

} }

Valid query Correct result

hero { name: Luke friends: [ { name: R2-D2 } { id: 1002 name: Han } ] }

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37 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Ground-Typed Normal Form

hero[episode: EMPIRE] { name friends {

  • n Droid { name }
  • n Human { id name }

} }

Ground-typed query Correct result

hero { name: Luke friends: [ { name: R2-D2 } { id: 1002 name: Han } ] }

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38 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Eliminatjng Redundancies

Rewriting rules for queries Every GraphQL query q can be rewritten into a query q’ that is i) non-redundant and ii) in ground-typed normal form, such that q ≡ q’ Advantage: field collection is not needed for non-redundant queries in ground-typed NF

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39 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Now to the Enumeratjon Problem

Let q be i) non-redundant and ii) in ground-typed normal form Result of q can be produced symbol by symbol with only constant time between symbols Time to produce the complete query result depends linearly on the size of this result

hero { friends: [ { name:R2-D2} ] }

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Complexity Analysis

Result Size

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41 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Results of GraphQL queries can be huge

start { knows { knows { … { knows { name } }… } } } Alice appears 2N times in the result

2N times

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42 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Huge results in practjce: Github’s GraphQL API

Owners of first five repos that user “danbri” contributes to, and the owners of first five repos that they contribute to, and so on...

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43 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Result sizes can be computed effjciently!!!

Let q be i) non-redundant and ii) in ground-typed normal form Time to compute the size of the result

  • f q over a graph G depends linearly on

the product (size of q) × (size of G)

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44 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Result-Size Computatjon

start { advisor { univ { name } } friend { univ { name } } }

size(q, r) = 4 + size(q2 ,u) + size(q3 ,u) q2 q3

start: { … … } Result:

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45 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Result-Size Computatjon

start { advisor { univ { name } } friend { univ { name } } }

size(q, r) = 4 + size(q2 ,u) + size(q3 ,u) size(q2 ,u) = size(q3 ,u) = q3 q2

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46 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Result-Size Computatjon

start { advisor { univ { name } } friend { univ { name } } }

size(q, r) = 4 + size(q2 ,u) + size(q3 ,u) q3 size(q2 ,u) = 4 + size(q4 ,v) size(q3 ,u) = q4 q2

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47 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Result-Size Computatjon

start { advisor { univ { name } } friend { univ { name } } }

size(q, r) = 4 + size(q2 ,u) + size(q3 ,u) q3 size(q2 ,u) = 4 + size(q4 ,v) size(q3 ,u) = q5 size(q4 ,v) = 4 + size(q5 ,w) q4 q2

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48 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Result-Size Computatjon

start { advisor { univ { name } } friend { univ { name } } }

size(q, r) = 4 + size(q2 ,u) + size(q3 ,u) q3 size(q2 ,u) = 4 + size(q4 ,v) size(q3 ,u) = q5 size(q4 ,v) = 4 + size(q5 ,w) q4 size(q5 ,w) = 3 size(q5) = 3 q2

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49 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Result-Size Computatjon

start { advisor { univ { name } } friend { univ { name } } }

size(q, r) = 4 + size(q2 ,u) + size(q3 ,u) q3 size(q2 ,u) = 4 + size(q4 ,v) size(q3 ,u) = q5 size(q4 ,v) = 4 + size(q5 ,w) = 4 + 3 = 7 q4 size(q5 ,w) = 3 size(q4) = 7 size(q5) = 3 q2

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50 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Result-Size Computatjon

start { advisor { univ { name } } friend { univ { name } } }

size(q, r) = 4 + size(q2 ,u) + size(q3 ,u) q3 size(q2 ,u) = 4 + size(q4 ,v) = 11 size(q3 ,u) = q5 size(q4 ,v) = 4 + size(q5 ,w) = 4 + 3 = 7 q4 size(q5 ,w) = 3 size(q4) = 7 size(q5) = 3 size(q2) = 11 q2

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51 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Result-Size Computatjon

start { advisor { univ { name } } friend { univ { name } } }

size(q, r) = 4 + size(q2 ,u) + size(q3 ,u) q3 size(q2 ,u) = 4 + size(q4 ,v) = 11 size(q3 ,u)= 4 + size(q4 ,v) q5 size(q4 ,v) = 4 + size(q5 ,w) = 4 + 3 = 7 q4 size(q5 ,w) = 3 size(q4) = 7 size(q5) = 3 size(q2) = 11 q4 q2

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52 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Result-Size Computatjon

start { advisor { univ { name } } friend { univ { name } } }

size(q, r) = 4 + size(q2 ,u) + size(q3 ,u) q3 size(q2 ,u) = 4 + size(q4 ,v) = 11 size(q3 ,u)= 4 + size(q4 ,v) = 4 + 7 = 11 q5 size(q4 ,v) = 4 + size(q5 ,w) = 4 + 3 = 7 q4 size(q5 ,w) = 3 size(q4) = 7 size(q5) = 3 q4 size(q2) = 11 size(q3) = 11 q2

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53 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Result-Size Computatjon

start { advisor { univ { name } } friend { univ { name } } }

size(q, r) = 4 + size(q2 ,u) + size(q3 ,u) = 26 q3 size(q2 ,u) = 4 + size(q4 ,v) = 11 size(q3 ,u)= 4 + size(q4 ,v) = 4 + 7 = 11 q5 size(q4 ,v) = 4 + size(q5 ,w) = 4 + 3 = 7 q4 size(q5 ,w) = 3 size(q4) = 7 size(q5) = 3 size(q2) = 11 size(q3) = 11 q4 q2 11 11

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54 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Proposal for GraphQL Servers

First, compute the size of the result. If too big, reject query. Else, inform the size to the client, and Send the result byte by byte. (or use the size as basis of a billing model)

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Summary

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56 Olaf Hartjg – Fundamental Propertjes of the GraphQL Language

Our Results in a Nutshell

Formal definition of the language

  • Property Graph-like data model
  • Formal query semantics

Study of computational complexity (the language admits really efficient evaluation methods)

  • Evaluation problem is NL-complete
  • Enumeration of results is linear

Solution to the problem of large results

  • Efficient algorithm to compute result size
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