connected compounds
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The document discusses connected components labeling algorithms for graphs. It evaluates parallel algorithms on CPU and GPU architectures for different types of graphs. The key algorithms discussed are disjoint set union and depth first search. It proposes a simple auto-tuned approach to select the best technique for a given graph and evaluates the algorithms on real and synthetic datasets ranging from 1-7 million nodes.
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2. To find the successor of a node in a binary search tree, we take the right child. This operation has a runtime complexity of O(1).
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- 2. Studied implemented and evaluated various parallel algorithms for connected components labeling in graphs. Two Architectures CPU– (OpenMp) and (CUDA) Different types of graphs. Propose simple auto tuned approach for choosing best technique for a graph.
- 3. Motivation Definitions Basic Algorithm Optimizations Datasets and Experiments Auto tuning Future Scope
- 4. Identify vertices that form a connected set in a graph. Used in: Pattern Recognition Physics Biology Social Network Analysis
- 5. Image Processing Pattern Recognition Gesture Recognition Spee d Limit 40 Speed Limit 40 Spee d Limit 40
- 6. Disjoint Set Union Make Set Union Link Find Set Depth First Search
- 7. Directed tree of h = 1 Root points to itself All children point to the root Root is called the representative of a connected components.
- 8. ( I,J ) is an edge in the graph. If i and j are currently in differently trees. Merge the two trees in to one. Make representation of one, point to the representative of the other.
- 9. Merging two trees T1 and T2. Whose representative should be changed? Toss a coin and choose a winner Tree with lower index wins always Alternate between iterations (Even, Odd) Tree with greater height wins
- 10. Move a node higher in the tree. Single level Multi level Final Aim EXAMPLE: Singletons Hooking Point jumping
- 11. Single instance edge storage ( u,v ) is same as (u,v) Reduced Memory Footprint Smaller traversal overhead Unconditional Hooking Calling at appropriate iteration helps in decreasing the number of iterations.
- 12. Only form stars in every iteration. No overhead in determining if a node is part of a star.
- 13. Random graphs 1Mto 7M nodes, average degree 5 RMAT Graphs Synthetic Social Networking 1M to 7M nodes Real world Data Web graphs Google web Berkeley Stanford domains
- 14. Thank you!!!