Wedge A New Frontier for Pull-based Graph Processing. Samuel Grossman and Christos Kozyrakis Platform Lab Retreat June 8, 2018
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1 Wedge A New Frontier for Pull-based Graph Processing Samuel Grossman and Christos Kozyrakis Platform Lab Retreat June 8, 2018
2 Graph Processing Problems modelled as objects (vertices) and connections between them (edges) Examples: Internet (pages and hyperlinks) Social network (people and friendships) Roads and intersections Products and ratings 2
3 Graph Processing F L A I E C G B D H K J 3
4 Graph Processing F L A I E C G B D H K Repeat until convergence J 4
5 Graph Processing 5
6 Graph Processing 6
7 Graph Processing 7
8 Graph Processing 8
9 Graph Processing Frontier: set of active vertices 9
10 Graph Processing Frontier: set of active vertices 10
11 Graph Processing 11
12 Graph Processing: Push and Pull Push Pull Group by source vertex Group by destination vertex 12
13 Graph Processing: Push and Pull Better at utilizing the frontier Push Higher throughput Pull Read Group by source vertex Dominated by atomic updates Write Read Read Group by destination vertex Dominated by reads 13
14 Graph Processing: Hybrid Frameworks Pull Push Yes Start Frontier No Get the benefits of both Need to write the application twice Full Enough? No Empty? Yes Finish 14
15 My Work 1. Grazelle Pull Push Throughput Start Yes Frontier No 2. Wedge Redesigned to work for pull Full Enough? No Empty? Yes Finish 15
16 Wedge Software implementation of the new pull-based frontier optimization, integrated into Grazelle Can outperform the hybrid version of Grazelle by up to 10 To be open-sourced 16
17 Frontier Implementation Bit-mask, allocated with one bit per vertex 1 means active, 0 means inactive Two exist: one is being produced while the other is consumed An engine sets the bit to 1 for any vertex when it writes an updated value to it Easy to do for both push-based and pull-based engines 17
18 Frontier Consumption Frontier (1 bit per vertex) Edge List (Vector-Sparse) 18
19 Frontier Consumption: Push Frontier (1 bit per vertex) Push Edge List (Source-grouped) (Source-Grouped Vector-Sparse) 19
20 Frontier Consumption: Push Frontier (1 bit per vertex) Push Edge List (Source-grouped) (Source-Grouped Vector-Sparse) 20
21 Frontier Consumption: Push Frontier (1 bit per vertex) Push Edge List (Source-grouped) (Source-Grouped Vector-Sparse) 21
22 Frontier Consumption: Push Frontier (1 bit per vertex) Push Edge List (Source-grouped) (Source-Grouped Vector-Sparse) 22
23 Frontier Consumption: Push Frontier (1 bit per vertex) Push Done Edge List (Source-grouped) (Source-Grouped Vector-Sparse) 23
24 Frontier Consumption: Pull Frontier (1 bit per vertex) Pull Edge List (Destination-grouped) (Destination-Grouped Vector-Sparse) 24
25 Frontier Consumption: Pull Frontier (1 bit per vertex) Pull Edge List (Destination-grouped) (Destination-Grouped Vector-Sparse) 25
26 Frontier Consumption: Pull Frontier (1 bit per vertex) Pull Edge List (Destination-grouped) (Destination-Grouped Vector-Sparse) 26
27 Frontier Consumption: Pull Frontier (1 bit per vertex) Pull Edge List (Destination-grouped) (Destination-Grouped Vector-Sparse) 27
28 Frontier Consumption: Pull Frontier (1 bit per vertex) Pull Edge List (Destination-grouped) (Destination-Grouped Vector-Sparse) 28
29 Frontier Consumption: Pull Frontier (1 bit per vertex) Pull Edge List (Destination-grouped) (Destination-Grouped Vector-Sparse) 29
30 Frontier Consumption: Pull Frontier (1 bit per vertex) Pull Edge List (Destination-grouped) (Destination-Grouped Vector-Sparse) 30
31 Frontier Consumption: Pull Frontier (1 bit per vertex) Done Pull Edge List (Destination-grouped) (Destination-Grouped Vector-Sparse) 31
32 Speedup Graph Processing: Push vs. Pull Pull Push/Hybrid No use of frontier 5 Entirely frontier-driven Logarithmic PageRank Running Grazelle on uk-2007 graph Breadth-First Search 32
33 Speedup Graph Processing: Push vs. Pull Pull No use of frontier 5 Push/Hybrid Entirely frontier-driven 0.01 Logarithmic PageRank Running Grazelle on uk-2007 graph Breadth-First Search 33
34 Towards a Pull-Based Frontier
35 Towards a Pull-Based Frontier 4 Vertices 2 and 4 are added to the frontier
36 Towards a Pull-Based Frontier 4 The active edges of the graph: Insert vertices using the classic source orientation 36
37 Towards a Pull-Based Frontier 4 The active edges of the graph: Traverse using a destination orientation 37
38 Towards a Pull-Based Frontier 4 The active edges of the graph: million extra edges Traverse using a destination orientation 38
39 Towards a Pull-Based Frontier 4 The active edges of the graph: Filter out inactive edges for each vertex 39
40 Pull-Based Frontier Requirements Insert vertices using the classic source orientation Traverse using a destination orientation Filter out inactive edges for each vertex 40
41 Wedge Frontier An edge-oriented frontier bit-mask Each bit represents a small number of edges in the destinationgrouped edge list 41
42 Wedge Frontier An edge-oriented frontier bit-mask Filter out inactive edges for each vertex Each bit represents a small number of edges in the destinationgrouped edge list Traverse using a destination orientation 42
43 Hybrid Functional Overview Pull Push Yes Start No Full Enough? No Empty? Yes Finish 43
44 Wedge Functional Overview Insert vertices using the classic source orientation Pull Yes Start Wedge No Full Enough? No Empty? Yes Finish 44
45 Wedge Operation foreach vertex v in source_oriented_frontier { // activate the vertex activate_vertex(v, wedge_frontier); } Sets the correct bits in the Wedge frontier 45
46 Hybrid Data Structures Pull Destination-Grouped Edge List Push Source-Grouped Edge List In-edges grouped by destination vertex Out-edges grouped by source vertex 46
47 Wedge Data Structures Pull Destination-Grouped Edge List Push Source-Grouped Edge List In-edges grouped by destination vertex Out-edges grouped by source vertex 47
48 Wedge Data Structures Pull Destination-Grouped Edge List Wedge Source-Grouped Edge Index In-edges grouped by destination vertex Bit positions in the Wedge frontier, grouped by source 48
49 Evaluation Scope Grazelle + Wedge is compared with the hybrid version of Grazelle Three applications: Single-Source Shortest Path, Breadth-First Search, and Connected Components Running on a single Intel Xeon E v3 processor 12 physical cores / 24 logical cores 49
50 Relative Execution Time Single-Source Shortest Path Pull Engine Improvement Grazelle (Pull) Grazelle (Hybrid) Grazelle + Wedge dimacs-usa livejournal twitter-2010 Grazelle + Wedge does better than just closing the performance gap! 50
51 Relative Execution Time Single-Source Shortest Path Zoomed In: Grazelle (Hybrid) vs Grazelle + Wedge Grazelle (Hybrid) Grazelle + Wedge (Pull) Grazelle + Wedge (Wedge) 10 dimacs-usa livejournal twitter
52 Relative Execution Time Breadth-First Search Pull Engine Improvement Grazelle (Pull) Grazelle (Hybrid) Grazelle + Wedge dimacs-usa livejournal twitter
53 Relative Execution Time Breadth-First Search Zoomed In: Grazelle (Hybrid) vs Grazelle + Wedge Grazelle (Hybrid) Grazelle + Wedge (Pull) Grazelle + Wedge (Wedge) % dimacs-usa livejournal twitter
54 Relative Execution Time Connected Components Pull Engine Improvement Grazelle (Pull) Grazelle (Hybrid) Grazelle + Wedge dimacs-usa livejournal twitter
55 Relative Execution Time Connected Components Zoomed In: Grazelle (Hybrid) vs Grazelle + Wedge Grazelle (Hybrid) Grazelle + Wedge (Pull) Grazelle + Wedge (Wedge) dimacs-usa livejournal twitter
56 Conclusion Eliminated the only benefit that a push engine had over a pull engine; the push engine is now obsolete! Implemented in software and integrated into Grazelle Can outperform the hybrid version of Grazelle by up to 10 To be open-sourced 56
57 Thank You Questions?
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