ArrayFire Graph : Dynamic Graph Library for GPUs Kumar Aatish - - PowerPoint PPT Presentation

ArrayFire Graph :

Dynamic Graph Library for GPUs

Kumar Aatish

ArrayFire

Domains

• Computer Vision
• Machine Learning
• Image Processing
• Computer Graphics

Industries

• Defense
• Oil and Gas
• Finance
• Media
• Accelerating computation
• HPC consulting for 10 years
• Maintain open source ArrayFire Library

Outline

• Static Graphs
• Dynamic Graphs
• AF Graph

○ Insertion ○ Deletion ○ SSSP ○ BFS ○ Out Of Core

What is a (Static) Graph?

• G = (V,E). Set of Vertices and Edges
• Edges = relationship between vertices
• Metadata

Snapshot of relationships between entities

1 2 3

What is a (Static) Graph?

2 6 8 1 2 3 Offsets Adjacency Lists

CSR Data Structure

1 2 3 3 1 2 1 2 3

What is a Dynamic Graph?

• G = (V,E). Set of Vertices and Edges
• Edges = relationship between vertices
• Metadata

Interactions/Relationships can change

• Vertices
• Edge
• Edge Weights
• etc.

1 2 3 4 5 6

What is a Dynamic Graph?

2 6 8 1 2 3 Offsets Adjacency Lists

CSR Data Structure Cannot handle insertions/removal

1 2 3 3 1 2 1 2 3

ArrayFire Graph

• GPU Optimized Dynamic Data Structure

○ Fast Insertions, Updates, Deletions ○ Tracks weights and temporal metadata ○ Optimized for GPU cache locality

• Minimize CPU Intervention
• Handles out of core graph operations
• Performant Graph Analytic Algorithms

○ BFS ○ SSSP ○ PageRank ○ and more soon

ArrayFire Graph

adjacencyU adjacencyV v u adjacencyU adjacencyV v u

• Conceptually similar to CSR
• Algorithms therefore easily portable

ArrayFire Graph

• Memory manager to improve performance
• Requires user defined upper limit on vertex degree

ArrayFire Graph

• Vertices with greater degree than limit?

○ Create zero weight edge from VB to empty vertex VE ○ Add edges to VE ○ User responsible for resolution ○ Will be done automatically in future

Insertion

• Consolidate Edge Inputs

○ Remove duplicates ○ Resolve weight/temporal metadata

SRC DST W T First T Last U V w1 TF1 TL1 U V w2 TF2 TL2 U V

• p(w1, w2)

min(TF1, TF2) max(TL1, TL2)

Insertion

• Update

○ Metadata ○ Adjacency Lists

Update—Adjacency List

Add edges to active vertices

• Identify active vertices
• Expand adjacency list size
• Copy new edges

Benchmark—Update Adjacency List

Graph Vertices (M) Edges(M) ldoor 0.952 45.5 soc-LiveJournal1 4.8 69 cage15 5.2 94 kron_g500-logn21 2 201 uk-2002 18.5 523

Benchmark graphs takes from [1] and [2]

Deletion

SSSP

Benchmarked against nvGraph[3]

• GPU Static Library
• NVIDIA Tesla P100 16 GB

Benchmark—SSSP

Graph Vertices(M) Edges(M) eu-2005 0.860 32 coPapersDBLP 0.540 30.5 in-2004 1.4 27.2 ldoor 0.950 45.5 road_central 14.0 33.8 road_usa 23.9 57.7

Benchmark—SSSP

Graph Vertices(M) Edges(M) eu-2005 0.860 32 coPapersDBLP 0.540 30.5 in-2004 1.4 27.2 ldoor 0.950 45.5 road_central 14.0 33.8 road_usa 23.9 57.7

BFS

Graph Vertices(M) Edges(M) ldoor 0.950 45.5 soc-LiveJournal1 4.8 69 cage15 5.2 94 kron_g500-logn21 2 201 uk-2002 18.5 523

Out of Core

• Insertion
• Graph Analytics Functions
• Maximum edge count on device
• Maintain adjacency list on host memory

Out of Core

• Identify active remote vertices
• Exchange

○ Inactive local vertices ○ Active remote vertices

• Work on current batch of local active vertices
• Repeat

Benchmark—Out of Core

• Benchmarked on road_central [1] (V : 14M, E : 33.8 M)
• Insertion and BFS
• Nvidia Tesla K40 12 GB, Host Memory : DDR3 1333 Mhz 8GB

Summary

• Great dynamic graph creation performance
• Highly performant graph algorithms
• Can benefit from advances in static graph algorithms
• Out of Core support

Future Plans

• Multi-GPU implementation near completion
• Add support for multiple edge types
• Add user queries for filtering graph by time stamps, edge types, etc.
• Avoid temporal or static metadata when user does not require them

Contact Us

ArrayFire.com Speaker : Kumar Aatish (kumar@ArrayFire.com) Sales : Scott Blakeslee (sales@ArrayFire.com)

• We are exploring use cases for

real-world applications

• Interested in AFGraph for your

application?

• Contact us to tailor it to your

needs

References

[1] D. A. Bader, H. Meyerhenke, P. Sanders, and D. Wagner, Eds., Graph Partitioning and Graph Clustering. 10th DIMACS Implementation Challenge Workshop, ser. Contemporary Mathematics, no. 588, 2013. [2] Stanford Network Analysis Package, 2012 (accessed April 2012). [Online]. Available: snap.stanford.edu/data/ [3] NVIDIA, “nvGraph,” 2016. developer.nvidia.com/nvgraph