1. Improving Parallelism in Structural Data Mining Min Cai, Istvan Jonyer, Marcin Paprzycki Computer Science Department, Oklahoma State University, Stillwater, Oklahoma 74078, U.S.A.

2. Who am I?  Min Cai: cmin@cs.okstate.educmin@cs.okstate.edu Ph.D. Student of Computer Science Department at Oklahoma State University Research Interests:  Parallel and distributed computing  Data Mining

3. Introduction  Data warehouses of increasing size  Data mining  technique for discovering interesting properties in data structural data mining  data represented as a graph  aim  substructure discovery  finding “interesting” and recurring subgraphs in a labeled graph

4. SUBDUE (1)  Discovers substructures utilizing minimum description length (MDL) principle Cook, D.J., Holder, L.B., G alal, G., Maglothin, R.: Approaches to Parallel Graph-Based Knowledge Discovery. Journal of Parallel and Distributed Computing, 61(3) (2001) 427-446  Data objects  graph vertices  Relationships  graph edges  Substructure  connected subgraph  NOTE  graph algorithms are notorious for long execution times

5. SUBDUE (2)  Algorithm  two basic steps substructure discovery  apply minimal description length (MDL) principle to find the “best” / “most important” structure in the graph  possibly stop here  this is the answer substructure replacement  replace the substructure found in the first step by a single vertex and repeat the process results  single substructure  hierarchy of substructures

6. Parallel SUBDUE  Data-parallel approach  Graph divided into subgraphs and send to separate processor  Processors find their best structure and communicate with the rest  The best overall substructure is found  Hierarchical process can be repeated

7. MPI-SUBDUE  Graph divided into subgraphs using METIS  point-to-point communications (MPI_Send and MPI_Recv) used to communicate between processors NOTE  best structure in data set “7” may be dreadful when confronted with data set “18”  Galal, G.M., Cook, D.J., Holder, L.B.: Improving Scalability in a Knowledge Discovery System by Exploiting Parallelism In the Proceedings of the Third International Conference on Knowledge Discovery and Data Mining (1997) 171-174

8. NEW-MPI-SUBDUE  Improvements use PARMETIS to divide the initial graph use global communication (MPI_Allgatherv) use binary summation  YES, these changes do not look like much

9. NEW-MPI-SUBDUE Spawn P(0), P(1), P(2),..., P(n) Apply PARMETIS to partition G into n partitions for all P(i) where 1 ≤ i ≤ n do discover the best substructure in partition broadcast best substructure to all other processors evaluate best substructure and broadcast results parallel-binary summation of results to find the best overall partition P(0) finds the best overall structure

10. EXPERIMENTAL SETUP  Mutagenesis data from OxUni datasets collected in order to predict mutagenicity of aromatic and heteroaromatic nitro compounds  Graph 1  2844 vertices and 2883 edges  Graph 2  2896 vertices and 2934 edges  Graph 3  22268 vertices and 22823 edges  16 node cluster (32 processors)  two AMD Athlon MP 1800+ (1.6GHz) CPUs, 2 GB of DDR SDRAM, full-backplane Gigabit Ethernet switch  RedHat Linux 9.0, MPICH, Portland Group C compiler 5.0-2

11. EXPERIMENTAL RESULTS I

12. EXPERIMENTAL RESULTS II

13. EXPERIMENTAL REULTS III

14. COMMENTS  Graphs 1 and 2 that were large in 2000 are small and “ useless ” today  Graph 3 gives realistic performance picture  gains about 33%  Speedup over original SUBDUE  268 on 32 processors for Graph 3 this IS “ cheating ” as some information may be lost due to graph partitioning but …  Graph partitioning and balancing matter

15. THE END THANK YOU!