Venkatram Ramanathan 1

Motivation Evolution of Multi-Core Machines and the challenges Background: MapReduce and FREERIDE Co-clustering on FREERIDE Experimental Evaluation Conclusion 2

Performance Increase: Increased number of cores with lower clock frequencies Cost Effective Scalability of performance HPC Environments – Cluster of Multi- Cores 3

Multi-Level Parallelism Within Cores in a node – Shared Memory Parallelism - Pthreads, OpenMP Within Nodes – Distributed Memory Parallelism - MPI Achieving Programmability and Performance – Major Challenge 4

Possible solution Use higher-level/restricted APIs Reduction based APIs Map-Reduce Higher-level API Program Cluster of Multi-Cores with 1 API Expressive Power Considered Limited Expressing computations using reduction-based APIs 5

MapReduce Map (in_key,in_value) -> list(out_key,intermediate_value) Reduce(out_key,list(intermediate_value) -> list(out_value) FREERIDE Users explicitly declare Reduction Object and update it Map and Reduce steps combined Each data element – processed and reduced before next element is processed 6

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Involves simultaneous clustering of rows to row clusters and columns to column clusters Maximizes Mutual Information Uses Kullback-Leibler Divergence 8

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Input matrix and its transpose pre-computed Input matrix and transpose Divided into files Distributed among nodes Each node - same amount of row and column data rowCL and colCL – replicated on all nodes Initial clustering Round robin fashion - consistency across nodes 11

In Preprocessing, pX and pY – normalized by total sum Wait till all nodes process to normalize Each node calculates pX and pY with local data Reduction object updated partial sum, pX and pY values Accumulated partial sums - total sum pX and pY normalized xnorm and ynorm calculated in second iteration as they need total sum 12

Compressed Matrix of size #rowclusters x #colclusters, calculated with local data Sum of values of values of each row cluster across each column cluster Final compressed matrix -sum of local compressed matrices Local compressed matrices – updated in reduction object Produces final compressed matrix on accumulation Cluster Centroids calculated 13

Reassign clustering Determined by Kullback-Leibler divergence Reduction object updated Compute compressed matrix Update reduction object Column Clustering – similar Objective function – finalize Next iteration 14

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Algorithm - same for shared memory, distributed memory and hybrid parallelization Experiments conducted 2 clusters env1 Intel Xeon E5345 Quad Core Clock Frequency 2.33 GHz Main Memory 6 GB 8 nodes env2 AMD Opteron 8350 CPU 8 Cores Main Memory 16 GB 4 Nodes 17

 2 Datasets  1 GB Dataset  Matrix Dimensions 16k x 16k  4 GB Dataset  Matrix Dimensions 32k x 32k  Datasets and transpose  Split into 32 files each (row partitioning)  Distributed among nodes  Number of row and column clusters: 4 18

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Preprocessing stage – bottleneck for smaller dataset – not compute intensive Speedup with Preprocessing : Speedup without Preprocessing: Preprocessing stage scales well for Larger dataset – more computation Speedup is the same with and without preprocessing. Speedup for larger dataset :

FREERIDE Offers the Following Advantages: No need for loading data in custom file-systems C/C++ based framework Much better performance (comparison for other algorithms) Co-clusterings can be viewed as generalized reduction Implementing them on FREERIDE Speedup of 21 on 32 cores. 23