The More the Merrier: Efficient Multi-Source Graph Traversal

Transcription

1 The More the Merrier: Efficient Multi-Source Graph Traversal Manuel Then *, Moritz Kaufmann *, Fernando Chirigati, Tuan-Anh Hoang-Vu, Kien Pham, Huy T. Vo, Alfons Kemper *, Thomas Neumann * * Technische Universität München, New York University

2 Outline Motivation Challenges Goals Multi-Source BFS Evaluation Summary The More the Merrier: Efficient Multi-Source Graph Traversal 2

3 Motivation Graph traversal vital part of graph analytics - BFS, DFS, Neighbor traversals, Random walks, The More the Merrier: Efficient Multi-Source Graph Traversal 3

4 Motivation Graph traversal vital part of graph analytics - BFS, DFS, Neighbor traversals, Random walks,... Often multiple BFS traversals necessary to compute results - Closeness centrality, Shortest paths, The More the Merrier: Efficient Multi-Source Graph Traversal 4

5 Motivation Graph traversal vital part of graph analytics - BFS, DFS, Neighbor traversals, Random walks,... Often multiple BFS traversals necessary to compute results - Closeness centrality, Shortest paths,... Real-world graphs often are small-world networks - Social networks, Web graphs, Communication networks The More the Merrier: Efficient Multi-Source Graph Traversal 5

6 Motivation Graph traversal vital part of graph analytics - BFS, DFS, Neighbor traversals, Random walks,... Often multiple BFS traversals necessary to compute results - Closeness centrality, Shortest paths,... Real-world graphs often are small-world networks - Social networks, Web graphs, Communication networks Subject of this talk: efficiently run multiple BFSs on real-world graphs The More the Merrier: Efficient Multi-Source Graph Traversal 6

7 Challenges Random data access intrinsic to graph traversal algorithms - bad cache behavior, frequent CPU stalls The More the Merrier: Efficient Multi-Source Graph Traversal 7

8 Challenges Random data access intrinsic to graph traversal algorithms - bad cache behavior, frequent CPU stalls Single bit accesses waste memory bandwidth - e.g. for BFS seen bitmaps The More the Merrier: Efficient Multi-Source Graph Traversal 8

9 Challenges Random data access intrinsic to graph traversal algorithms - bad cache behavior, frequent CPU stalls Single bit accesses waste memory bandwidth - e.g. for BFS seen bitmaps Independent BFS runs redundantly visit vertices multiple times The More the Merrier: Efficient Multi-Source Graph Traversal 9

10 Challenge - Redundant visits Example: BFSs in a simple graph Initial BFS The More the Merrier: Efficient Multi-Source Graph Traversal 10

11 Challenge - Redundant visits Example: BFSs in a simple graph Initial Iteration 1 BFS The More the Merrier: Efficient Multi-Source Graph Traversal 11

12 Challenge - Redundant visits Example: BFSs in a simple graph Initial Iteration 1 Iteration 2 BFS The More the Merrier: Efficient Multi-Source Graph Traversal 12

13 Challenge - Redundant visits Example: BFSs in a simple graph Initial Iteration 1 Iteration 2 BFS 1 BFS The More the Merrier: Efficient Multi-Source Graph Traversal 13

14 Challenge - Redundant visits Example: BFSs in a simple graph Initial Iteration 1 Iteration 2 BFS 1 BFS The More the Merrier: Efficient Multi-Source Graph Traversal 14

15 Challenge - Redundant visits Example: BFSs in a simple graph Initial Iteration 1 Iteration 2 BFS 1 BFS The More the Merrier: Efficient Multi-Source Graph Traversal 15

16 Challenge - Redundant visits (cont.) Redundant vertex visits for 512 BFSs on LDBC 1M social network graph After a few iterations, many redundant visits in small-world networks The More the Merrier: Efficient Multi-Source Graph Traversal 16

17 Goals Leverage knowledge that multiple BFS traversal are run The More the Merrier: Efficient Multi-Source Graph Traversal 17

18 Goals Leverage knowledge that multiple BFS traversal are run Optimize data access patterns - embrace memory accesses instead of trying to hide them - CPUs always fetch full cache lines - use all of them The More the Merrier: Efficient Multi-Source Graph Traversal 18

19 Goals Leverage knowledge that multiple BFS traversal are run Optimize data access patterns - embrace memory accesses instead of trying to hide them - CPUs always fetch full cache lines - use all of them Avoid redundant computation and vertex visits - touch vertex information as rarely as possible The More the Merrier: Efficient Multi-Source Graph Traversal 19

20 Multi-Source BFS Concurrently run many independent BFS traversals on the same graph - 100s of BFSs on a single CPU core The More the Merrier: Efficient Multi-Source Graph Traversal 20

21 Multi-Source BFS Concurrently run many independent BFS traversals on the same graph - 100s of BFSs on a single CPU core X + X visit seen next The More the Merrier: Efficient Multi-Source Graph Traversal 21

22 Multi-Source BFS Concurrently run many independent BFS traversals on the same graph - 100s of BFSs on a single CPU core Store concurrent BFSs state as 3 bitsets per vertex visit seen next Represent BFS traversal as SIMD bit operations on these bitsets The More the Merrier: Efficient Multi-Source Graph Traversal 22

23 Multi-Source BFS Concurrently run many independent BFS traversals on the same graph - 100s of BFSs on a single CPU core Store concurrent BFSs state as 3 bitsets per vertex visit seen next Represent BFS traversal as SIMD bit operations on these bitsets Fully utilize cache line-sized memory accesses of modern CPUs Efficiently share traversals whenever possible - neighbors traversed only once for all concurrent BFSs The More the Merrier: Efficient Multi-Source Graph Traversal 23

24 Multi-Source BFS - Example Initial The More the Merrier: Efficient Multi-Source Graph Traversal 24

25 Multi-Source BFS - Example Initial Iteration The More the Merrier: Efficient Multi-Source Graph Traversal 25

26 Multi-Source BFS - Example Initial Iteration The More the Merrier: Efficient Multi-Source Graph Traversal 26

27 Multi-Source BFS - Example Initial Iteration The More the Merrier: Efficient Multi-Source Graph Traversal 27

28 Multi-Source BFS - Example Initial Iteration 1 Iteration The More the Merrier: Efficient Multi-Source Graph Traversal 28

29 Multi-Source BFS - Example Initial Iteration 1 Iteration The More the Merrier: Efficient Multi-Source Graph Traversal 29

30 Multi-Source BFS - Example Initial Iteration 1 Iteration The More the Merrier: Efficient Multi-Source Graph Traversal 30

31 Multi-Source BFS - Further Improvements Aggregated neighbor processing - reduce number of random writes Batching heuristics for maximum sharing Direction-optimizing Prefetching... see paper The More the Merrier: Efficient Multi-Source Graph Traversal 31

32 Evaluation - The More the Merrier The More the Merrier: Efficient Multi-Source Graph Traversal 32

33 Evaluation MS-BFS-based closeness centrality. 4x Intel Xeon E7-4870v2, 1TB The More the Merrier: Efficient Multi-Source Graph Traversal 33

34 Evaluation MS-BFS-based closeness centrality. 4x Intel Xeon E7-4870v2, 1TB The More the Merrier: Efficient Multi-Source Graph Traversal 34

35 Summary Making graph traversals aware of each other can lead to substantial performance increase Multi-Source BFS (MS-BFS) runs multiple independent BFSs on the same graph concurrently on a single CPU and shares their traversals. MS-BFS shows x speedup over existing single-source BFSs The More the Merrier: Efficient Multi-Source Graph Traversal 35

36 Backup The More the Merrier: Efficient Multi-Source Graph Traversal 36

37 Backup The More the Merrier: Efficient Multi-Source Graph Traversal 37