Connected Components Labeling
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Connected Components Labeling
- 1. Connected Components Labeling Term Project: CS395T, Software for Multicore Processors Hemanth Kumar Mantri Siddharth Subramanian Kumar Ashish
- 2. Big Picture • Studied, Implemented and Evaluated various parallel algorithms for Connected Components Labeling in Graphs • Two Architectures – CPU (OpenMP) and GPU (CUDA) • Different types of graphs • Propose simple Autotuned approach for choosing best technique for a graph
- 3. Our Menu • Motivation • Definitions • Basic Algorithms • Optimizations • Datasets and Experiments • Autotuning • Future Scope
- 4. Our Menu • Motivation • Definitions • Basic Algorithms • Optimizations • Datasets and Experiments • Autotuning • Future Scope
- 5. Why Connected Components? • Identify vertices that form a connected set in a Graph • Used in: – Pattern Recognition – Physics • Identify Clusters – Biology • DNA components – Social Network Analysis
- 6. Applications • Physics • Image Processing – Identify Clusters • Biology – Components in DNA • Pattern Recognition • Gesture Recognition
- 7. Sequential Implementation • Disjoint Set Union – MakeSet – Union – Link – FindSet • Depth First Search
- 8. Our Menu • Motivation • Definitions • Basic Algorithms • Optimizations • Datasets and Experiments • Autotuning • Future Scope
- 9. Rooted Star • Directed tree of h = 1 • Root points to itself • All children point to the root • Root is called the representative of a connected component
- 10. Hooking • (i, j) is an edge in the graph • If i and j are currently in different trees • Merge the two trees in to one • Make representative of one, point to the representative of the other
- 11. Breaking Ties • Merging two trees T1 and T2, • Whose representative should be changed? – Toss a coin and choose a winner – Tree with lower(higher) index wins always – Alternate between iterations (Even, Odd) – Tree with greater height wins
- 12. Pointer Jumping • Move a node higher in the tree • Single Level • Multi Level • Final Aim – Form Rooter Stars
- 13. EXAMPLE
- 15. Hooking
- 16. Pointer Jumping
- 17. Our Menu • Motivation • Definitions • Basic Algorithms • Optimizations • Datasets and Experiments • Autotuning • Future Scope
- 18. SV Algorithm
- 20. Our Menu • Motivation • Definitions • Basic Algorithms • Optimizations • Datasets and Experiments • Autotuning • Future Scope
- 21. CPU Optimizations • Single Instance edge storage – (u, v) is same as (v, u) – Reduced Memory Footprint • Support large graphs – Smaller traversal overhead • Every iteration needs to see all edges • Unconditional Hooking – Calling at appropriate iteration helps in decreasing the number of iterations
- 22. Multi Level Pointer Jumping • Only form stars in every iteration • No overhead in determining if a node is part of a star
- 23. OpenMP Scheduling • Static • Dynamic • Guided Scheduling – Gave best performance
- 24. Hide Inactive Edges • If two ends of an edge are part of same connected component, hide them • Save time for next iterations
- 25. For GPU • Different from PRAM Model – Threads are grouped into Thread Blocks – Requires explicit synchronization across TBs • 64 bit for representing an edge – Reduced Random Reads – Read edge in single memory transaction • In first Iteration hook neighbors instead of their parents – Reduced irregular reads • GeForce GTX 480 – Use 1024 threads per block
- 26. Our Menu • Motivation • Definitions • Basic Algorithms • Optimizations • Datasets and Experiments • Autotuning • Future Scope
- 27. Datasets • Random Graphs – 1M to 7M nodes, average degree 5 • RMAT Graphs – Synthetic Social Networks – 1M to 7M nodes • Real World Data (From SNAP, by Leskovec) – Road Networks: • California • Pennsylvania • Texas – Web Graphs • Google Web • Berkeley-Stanford domains
- 28. Execution Environment • CPU (Faraday): A 48 core Intel Xeon E7540 (2.00 GHz), with 18 MB cache, 132 GB RAM • GPU (Gleim): GeForce GTX 480 with 1.5 GB shared memory and 177.4 GB/s memory bandwidth. It was attached to a Quadcore Intel Xeon CPU (2.40 GHz) running CUDA Toolkit/SDK version 4.1. The host machine had 6 GB RAM.
- 29. Random Graphs CPU – Scaling with threads
- 30. RMAT-Graphs CPU – Scaling with threads
- 31. Web graphs CPU – Scaling with threads
- 32. Road network CPU – Scaling with threads
- 33. Random graph – Scaling with vertices
- 34. R-MAT – Scaling with vertices
- 35. GPU on Random and RMAT
- 37. Our Menu • Motivation • Definitions • Basic Algorithms • Optimizations • Datasets and Experiments • Analysis and Autotuning • Future Scope
- 38. What is Autotuning? • Automatic process for selecting one out of several possible solutions to a computational problem. • The solutions may differ in the – algorithm (quicksort vs selection sort) – implementation (loop unroll). • The versions may result from – transformations (unroll, tile, interchange) • The versions could be generated by – programmer manually (coding or directives) – compiler automatically
- 39. How? • Have various ways to do hooking, pointer jumping • Characterize graphs based on some features • Employ the best technique for a given graph
- 40. Performance Deciders • Number of Iterations – Each iteration needs to traverse the whole set of edges • Pointer Jumps – Higher the root node, more the work • Trade off – More iterations and Single level jump in each iteration – Less iterations with Multi Level jumps
- 41. Choosing Right Approach • More iterations and Single level jump in each iteration – Good for graphs with less edges and less diameter – If edges is constant, works well for social networks • Less iterations with Multi Level jumps – Good for graphs with large diameter – Very good scalability – Good for GPU – Road Network
- 42. Graph Types • Road Networks – Large diameter – Forms very deep trees • R-MAT and Social Networks – More Cliques • Web Graphs – Dense graphs
- 43. Other Findings • Multilevel Pointer Jumping – Less number of iterations – Star-check is not required – Good for high diameter graphs – Good scalability for R-MAT graphs • Even-Odd Hooking – Works well with random and R-MAT graphs – Performance quite similar to Optimized SV in most cases
- 44. Our approach • Given: A graph whose type is unknown • Training phase: Generate models of known graph types by running and profiling the feature values • Test phase: – Run initial algorithm for few iterations – Find the graph similar to current profile – Switch to best algorithm for that graph type
- 45. Feature selection • Pointer jumpings per hook – Captures the amount of work per iteration • Percentage of pointer jumpings done per iteration – Might give insights about type of graph – Problem: Needs information from future iterations
- 46. Effectiveness of features – Pointer jumpings per hook
- 47. Percentage of pointer jumpings
- 48. Percentage of pointer jumpings (modified)
- 49. Simple tool • parallel_ccl – Optimizations supplied as command line args
- 50. Our Menu • Motivation • Definitions • Basic Algorithms • Optimizations • Datasets and Experiments • Analysis and Autotuning • Future Scope
- 51. Future Scope • More sophisticated Autotuning – Reduce profiling overhead – Introduce more intelligent modeling based on better features for the graphs • Heterogeneous Algorithm – Start with running on GPU – Parallelism falls after a few iterations • Less active edges – Switch to CPU to save power