The More the Merrier: Efficient Multi-Source Graph Traversal Manuel - - PowerPoint PPT Presentation

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The More the Merrier: Efficient Multi-Source Graph Traversal Manuel - - PowerPoint PPT Presentation

Dec 16, 2022 120 likes •492 views

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 Universit t M

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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

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2015-09-01 The More the Merrier: Efficient Multi-Source Graph Traversal 2

Outline

  • Motivation
  • Challenges
  • Goals
  • Multi-Source BFS
  • Evaluation
  • Summary

The More the Merrier: Efficient Multi-Source Graph Traversal

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Motivation

  • Graph traversal vital part of graph analytics
  • BFS, DFS, Neighbor traversals, Random walks, ...
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2015-09-01 The More the Merrier: Efficient Multi-Source Graph Traversal 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, ...
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2015-09-01 The More the Merrier: Efficient Multi-Source Graph Traversal 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
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2015-09-01 The More the Merrier: Efficient Multi-Source Graph Traversal 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
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Challenges

  • Random data access intrinsic to graph traversal algorithms
  • bad cache behavior, frequent CPU stalls
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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
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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
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Challenge - Redundant visits

Example: BFSs in a simple graph Initial BFS1

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Challenge - Redundant visits

Example: BFSs in a simple graph Initial Iteration 1 BFS1

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Challenge - Redundant visits

Example: BFSs in a simple graph Initial Iteration 1 Iteration 2 BFS1

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Challenge - Redundant visits

Example: BFSs in a simple graph Initial Iteration 1 Iteration 2 BFS1 BFS2

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Challenge - Redundant visits

Example: BFSs in a simple graph Initial Iteration 1 Iteration 2 BFS1 BFS2

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Challenge - Redundant visits

Example: BFSs in a simple graph Initial Iteration 1 Iteration 2 BFS1 BFS2

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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
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Goals

  • Leverage knowledge that multiple BFS traversal are run
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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
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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
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Multi-Source BFS

  • Concurrently run many independent BFS traversals on the same graph
  • 100s of BFSs on a single CPU core
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Multi-Source BFS

  • Concurrently run many independent BFS traversals on the same graph
  • 100s of BFSs on a single CPU core

visit seen next

+

X X

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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
  • Represent BFS traversal as SIMD bit operations on these bitsets

visit seen next

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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
  • 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

visit seen next

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Multi-Source BFS - Example

Initial

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Multi-Source BFS - Example

Initial Iteration 1

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Multi-Source BFS - Example

Initial Iteration 1

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Multi-Source BFS - Example

Initial Iteration 1

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Multi-Source BFS - Example

Initial Iteration 1 Iteration 2

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Multi-Source BFS - Example

Initial Iteration 1 Iteration 2

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Multi-Source BFS - Example

Initial Iteration 1 Iteration 2

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Multi-Source BFS - Further Improvements

  • Aggregated neighbor processing
  • reduce number of random writes
  • Batching heuristics for maximum sharing
  • Direction-optimizing
  • Prefetching

... see paper

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Evaluation - The More the Merrier

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Evaluation

  • MS-BFS-based closeness centrality. 4x Intel Xeon E7-4870v2, 1TB
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Evaluation

  • MS-BFS-based closeness centrality. 4x Intel Xeon E7-4870v2, 1TB
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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 10-100x speedup over existing single-source BFSs
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Backup 1

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Backup 2