Connected Components Labeling
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This document summarizes a project on implementing and evaluating parallel algorithms for connected components labeling on graphs using CPU (OpenMP) and GPU (CUDA). It studied different graph types and architectures. It proposed a simple autotuning approach to choose the best technique for a given graph by characterizing graphs based on features and employing the best algorithm. It discussed motivations, definitions, basic algorithms, optimizations, experiments on datasets, and future work including more sophisticated autotuning and heterogeneous algorithms.
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