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A Lightweight Infrastructure for Graph Analytics
- 1. A Lightweight Infrastructurefor Graph Analytics Donald Nguyen Andrew Lenharth and Keshav Pingali The University of Texas at Austin
- 2. What is GraphAnalytics? • Algorithms to compute properties of graphs – Connected components, shortest paths, centrality measures, diameter, PageRank, … • Many applications – Google, path routing, friend recommendations, network analysis • Difficult to implement on a large scale – Data sets are large, data accesses are irregular – Need parallelismand efficient runtimes Bridges of Konigsberg The Social Network
- 3. Contributions • A lightweightinfrastructure for graph analytics based on improvements to the Galois system – Example: scalable priority scheduling • Orders of magnitude faster than third-party graph DSLs for many applications and inputs – Galois permits better algorithms to be written – Galois infrastructure more scalable 3
- 4. Outline 1. Abstraction forgraph analytics applications and implementation in Galois system 2. One piece of infrastructure: priority scheduling 3. Evaluation of Galois system versus graph analytics DSLs 4
- 5. Example: SSSP • Findthe shortest distance from source node to all other nodes in a graph – Label nodes with tentativedistance – Assume non-negativeedge weights • Algorithms – Chaotic relaxation O(2V) – Bellman-Ford O(VE) – Dijkstra’s algorithm O(E log V) • Uses priority queue – Δ-stepping • Uses sequence of bags to prioritize work • Δ=1, O(E log V) • Δ=∞, O(VE) • Different algorithms are different schedules for applying relaxations – SSSP needs priority scheduling for work efficiency 1 9 2 3 1∞ ∞ 0 1 9 4 3 1 3 Operator Edge relaxation ∞ 2 5
- 6. Example: SSSP • Findthe shortest distance from source node to all other nodes in a graph – Label nodes with tentativedistance – Assume non-negativeedge weights • Algorithms – Chaotic relaxation O(2V) – Bellman-Ford O(VE) – Dijkstra’s algorithm O(E log V) • Uses priority queue – Δ-stepping • Uses sequence of bags to prioritize work • Δ=1, O(E log V) • Δ=∞, O(VE) • Different algorithms are different schedules for applying relaxations – SSSP needs priority scheduling for work efficiency 1 9 2 3 1∞ ∞ 0 Active edge 1 9 4 3 1 3 Operator Edge relaxation ∞ 2 6
- 7. Example: SSSP • Findthe shortest distance from source node to all other nodes in a graph – Label nodes with tentativedistance – Assume non-negativeedge weights • Algorithms – Chaotic relaxation O(2V) – Bellman-Ford O(VE) – Dijkstra’s algorithm O(E log V) • Uses priority queue – Δ-stepping • Uses sequence of bags to prioritize work • Δ=1, O(E log V) • Δ=∞, O(VE) • Different algorithms are different schedules for applying relaxations – SSSP needs priority scheduling for work efficiency 1 9 2 3 1∞ ∞ 0 Active edge Neighborhood Activity 1 9 4 3 1 3 Operator Edge relaxation ∞ 2 7
- 8. Parallel Program =Operator + Schedule + Parallel Data Structure Algorithm 8
- 9. Parallel Program =Operator + Schedule + Parallel Data Structure • What is the operator? – Ligra, PowerGraph:only vertex programs – Galois: Unrestricted, may even morph graph by adding/removing nodes and edges • Where/When does it execute? – Autonomous scheduling: activities execute transactionally – Coordinated scheduling: activities execute in rounds • Read values refer to previous rounds • Multiple updates to the same location are resolved with reduction, etc. Algorithm 9
- 10. Parallel Program =Operator + Schedule + Parallel Data Structure • What is the operator? – Ligra, PowerGraph:only vertex programs – Galois: Unrestricted, may even morph graph by adding/removing nodes and edges • Where/When does it execute? – Autonomous scheduling: activities execute transactionally – Coordinated scheduling: activities execute in rounds • Read values refer to previous rounds • Multiple updates to the same location are resolved with reduction, etc. Algorithm 10
- 11. Parallel Program =Operator + Schedule + Parallel Data Structure • What is the operator? – Ligra, PowerGraph:only vertex programs – Galois: Unrestricted, may even morph graph by adding/removing nodes and edges • Where/When does it execute? – Autonomous scheduling: activities execute transactionally – Coordinated scheduling: activities execute in rounds • Read values refer to previous rounds • Multiple updates to the same location are resolved with reduction, etc. Algorithm 11
- 12. Parallel Program =Operator + Schedule + Parallel Data Structure • What is the operator? – Ligra, PowerGraph:only vertex programs – Galois: Unrestricted, may even morph graph by adding/removing nodes and edges • Where/When does it execute? – Autonomous scheduling: activities execute transactionally – Coordinated scheduling: activities execute in rounds • Read values refer to previous rounds • Multiple updates to the same location are resolved with reduction, etc. Algorithm ba c 12
- 13. Galois System Parallel Program= Operator + Schedule + Parallel Data Structure Operators Schedules Data StructureAPI Calls Schedulers Data Structures AllocatorThread Primitives Multicore User Program Galois System 13
- 14. Outline 1. Abstraction forgraph analytics applications and implementation in Galois system 2. One piece of infrastructure: priority scheduling 3. Evaluation of Galois system versus DSLs 14
- 15. Galois Infrastructure forScheduling • Library of different schedulers – FIFO, LIFO, Priority, … – DSL for specifying scheduling policies • Nguyen and Pingali (ASPLOS ’11) 15
- 16. Priority Scheduling • Concurrentpriority queue – Implemented in TBB, java.concurrent – Does not scale: our tasks are very fine-grain • Sequence of bags – One bag per priority level – High overhead for finding non-empty, urgent- priority bags 16
- 17. Ordered by Metric(OBIM) • Sparse sequence of Bags – One Bag per priority level – To reduce synchronization • Sequence is replicated among cores • Bag is distributed between cores – To reduce overhead of finding work • A reduction tree over machine topology to get estimate of current urgent priority 17
- 18. Scheduling Bag c1 c2 Head Package1 18 Bag c1 c2 Head Package 2
- 19. Scheduling Bag c1 c2 Head Package1 19 Bag c1 c2 Head Package 2
- 20. Scheduling Bag c1 c2 Head Package1 20 Bag c1 c2 Head Package 2
- 21. Scheduling Bag c1 c2 Head Package1 21 Bag c1 c2 Head Package 2
- 22. Scheduling Bag c1 c2 Head Package1 22 Bag c1 c2 Head Package 2
- 23. Scheduling Bag c1 c2 Head Package1 23 Bag c1 c2 Head Package 2
- 24. Scheduling Bag c1 c2 Head Package1 24 Bag c1 c2 Head Package 2
- 25. Scheduling Bag c1 c2 Head Package1 25 Bag c1 c2 Head Package 2
- 26.
- 27. Priority Map 0 1 GlobalMap Local Maps Core 1 Core 2 Scheduling Bags 1 3 1 30 27
- 28. Priority Map 0 1 GlobalMap Local Maps Core 1 Core 2 Scheduling Bags 1 3 1 30 28
- 29. Priority Map 0 1 GlobalMap Local Maps Core 1 Core 2 Scheduling Bags 1 3 1 30 13 29
- 30. Priority Map 0 1 GlobalMap Local Maps Core 1 Core 2 Scheduling Bags 1 3 1 30 13 30
- 31. Priority Map 0 1 GlobalMap Local Maps Core 1 Core 2 Scheduling Bags 1 3 1 30 13 3 31
- 32. Priority Map 0 1 GlobalMap Local Maps Core 1 Core 2 Scheduling Bags 1 3 1 30 1 3 32
- 33. Priority Map 0 1 GlobalMap Local Maps Core 1 Core 2 Scheduling Bags 1 3 1 30 1 3 15 33
- 34. Priority Map 0 1 GlobalMap Local Maps Core 1 Core 2 Scheduling Bags 1 3 1 30 1 3 15 34
- 35. Priority Map 0 1 GlobalMap Local Maps Core 1 Core 2 Scheduling Bags 1 3 1 30 1 3 15 5 5 35
- 36. Priority Map 0 1 GlobalMap Local Maps Core 1 Core 2 Scheduling Bags 1 3 1 30 1 3 1 5 5 36
- 37. Outline 1. Abstraction forgraph analytics applications and implementation in Galois system 2. One piece of infrastructure: priority scheduling 3. Evaluation of Galois system versus graph analytics DSLs 37
- 38. Graph Analytics DSLs •Easy to implement their APIs on top of Galois system – Galois implementations called PowerGraph-g, Ligra-g, etc. – About 200-300 lines of code each 38 Ÿ GraphLab Low et al. (UAI ’10) Ÿ PowerGraph Gonzalez et al. (OSDI ’12) Ÿ GraphChi Kyrola et al. (OSDI ’12) Ÿ Ligra Shun and Blelloch (PPoPP ’13) Ÿ Pregel Malewicz et al. (SIGMOD ‘10) Ÿ …
- 39. Evaluation • Platform – 40-coresystem • 4 socket, Xeon E7-4860 (Westmere) – 128 GB RAM • Applications – Breadth-first search (bfs) – Connected components (cc) – Approximate diameter (dia) – PageRank (pr) – Single-source shortest paths (sssp) • Inputs – twitter50 (50 M nodes, 2 B edges, low-diameter) – road (20 M nodes, 60 M edges, high-diameter) • Comparison with – Ligra (shared memory) – PowerGraph (distributed) • Runtimes with 64 16-core machines (1024 cores) does not beat one 40-core machine using Galois 39
- 40. 40 Ligra runtime Galois runtime 1 10 100 1000 10000 1 10 100 1000 10000 bfscc dia pr sssp Ligra runtime Ligra⌫g runtime 1 2 1 2 4 6 bfs cc dia pr sssp Range <= 1 > 1
- 41. 41 Ligra runtime Galois runtime 1 10 100 1000 10000 1 10 100 1000 10000 bfscc dia pr sssp Ligra runtime Ligra⌫g runtime 1 2 1 2 4 6 bfs cc dia pr sssp Range <= 1 > 1
- 42. 42 PowerGraph runtime Galois runtime 1 10 100 1000 10000 1 10 100 1000 10000 bfscc dia pr sssp PowerGraph runtime PowerGraph⇠g runtime 1 2 1 2 4 6 bfs cc dia pr sssp
- 43. 43 PowerGraph runtime Galois runtime 1 10 100 1000 10000 1 10 100 1000 10000 bfscc dia pr sssp PowerGraph runtime PowerGraph⇠g runtime 1 2 1 2 4 6 bfs cc dia pr sssp
- 44. PowerGraph runtime Galois runtime 1 10 100 1000 10000 1 10 100 1000 10000 bfscc dia pr sssp PowerGraph runtime PowerGraph⇠g runtime 1 2 1 2 4 6 bfs cc dia pr sssp 44
- 45. PowerGraph runtime Galois runtime 1 10 100 1000 10000 1 10 100 1000 10000 bfscc dia pr sssp PowerGraph runtime PowerGraph⇠g runtime 1 2 1 2 4 6 bfs cc dia pr sssp • The best algorithm may require application- specific scheduling – Priority scheduling for SSSP • The best algorithm may not be expressible as a vertex program – Connected components with union-find • Autonomous scheduling required for high- diameter graphs – Coordinated scheduling uses many rounds and has too much overhead 45
- 46. PowerGraph runtime Galois runtime 1 10 100 1000 10000 1 10 100 1000 10000 bfscc dia pr sssp PowerGraph runtime PowerGraph⇠g runtime 1 2 1 2 4 6 bfs cc dia pr sssp • The best algorithm may require application- specific scheduling – Priority scheduling for SSSP • The best algorithm may not be expressible as a vertex program – Connected components with union-find • Autonomous scheduling required for high- diameter graphs – Coordinated scheduling uses many rounds and has too much overhead 46
- 47. PowerGraph runtime Galois runtime 1 10 100 1000 10000 1 10 100 1000 10000 bfscc dia pr sssp PowerGraph runtime PowerGraph⇠g runtime 1 2 1 2 4 6 bfs cc dia pr sssp • The best algorithm may require application- specific scheduling – Priority scheduling for SSSP • The best algorithm may not be expressible as a vertex program – Connected components with union-find • Autonomous scheduling required for high- diameter graphs – Coordinated scheduling uses many rounds and has too much overhead 47
- 48. See Paper For •More inputs, applications • Detailed discussion of performance results • More infrastructure: non-priority scheduling, memory management • Results for out-of-core DSLs 48
- 49. Summary • Galois programmingmodel is general – Permits efficient algorithms to be written • Galois infrastructure is lightweight • Simpler graph DSLs can be layered on top – Can perform better than existing systems • Download at http://iss.ices.utexas.edu/galois 49