Elixir

A System for Synthesizing Concurrent

Graph Programs

1

Motivation

• Performance of standard graph algorithms dependent on:

• Graph topology (diameter)

• Scheduling

• Architecture (SIMD/MIMD)

• …

• Elixir: high-level tool to generate optimal implementations

2

Specification

• Typed graph definition

• Operators with shape and value constraints define updates on subgraphs

• Statements: foreach, for i..range, iterate

• Scheduling operators restrict order

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4

Algorithms in Elixir

5

Scheduling operators

• Metric

– Define online priorities

• Group

– Co-schedule edges from same source

• Fuse

• Unroll

• Ordered/unordered

6

Example: unroll and group

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5 B

D

C

E 3

4

2

1

Example: unroll and group

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5 8

D

C

E 3

4

2

1

Synthesis

• Translated to C++, predefined graph types

• Worklists hold potential matching subgraphs

• Dynamic scheduling in OpenMP

• Enumerative exploration approach

– Tests a predefined set of combinations of unroll, grouping

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Matching subgraphs 1/2

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Matching subgraphs 2/2

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Evaluation 1/2

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Evaluation 2/2

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A Graph G…

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Conclusion

• “Does not rely on expert knowledge”

• High up-front effort to learn specification

• Bloated formalism

• Can beat hand-written implementations through intricate load-balancing

• No dynamic graphs supported

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