This document discusses parallelizing several algorithms and applications including k-means clustering, frequent itemset mining, integer programming, computer chess, and support vector machines (SVM). For k-means and frequent itemset mining, the algorithms can be parallelized by partitioning the data across processors and performing partial computations locally before combining results with an allreduce operation. Computer chess can be parallelized by exploring different game tree branches simultaneously on different processors. SVM problems involve large dense matrices that are difficult to solve in parallel directly due to their size exceeding memory; alternative approaches include solving smaller subproblems independently.

1. Parallel Computing 2007: Bring your own parallel application February 26-March 1 2007 Geoffrey Fox Community Grids Laboratory Indiana University 505 N Morton Suite 224 Bloomington IN [email_address]

2. Intel’s Application Stack Discussed here Rest mainly classic parallel computing

4. Problem used later in deterministic annealing version of K-Means

5. K-Means illustrated Again, the centers are moved to the centroids of the corresponding associated points. Now, the association is shown in more detail, once the centroids have been moved. Centers have been associated with the points and have been moved to the respective centroids Shows the initial randomized centers and a number of points a) b) c) d)

7. MPI Parallel Divkmeans clustering of PubChem AVIDD Linux cluster, 5,273,852 structures (Pubchem compound collection, Nov 2005) David Wild Indiana

12. Continuing the Intel Homework Set

14. Deterministically find cluster centers y j using “mean field approximation” – could use slower Monte Carlo

16. Annealing avoids local minima

33. Some Parallelization Results from “Parallel Software for Training Large Scale Support Vector Machines on Multiprocessor Systems” This paper reviews much previous work Super linear speedup in (a) due to extra memory