Combinatorial Scientific Computing and Petascale Simulation (CSCAPES) A SciDAC Institute Funded by DOE’s Office of Science Investigators Alex Pothen, Florin Dobrian, and Assefaw Gebremedhin (ODU) Erik Boman, Karen Devine, and Bruce Hendrickson (SNL) Paul Hovland, Boyana Norris, and Jean Utke (ANL) Umit Catalyurek (OSU) Michelle Strout (CSU)

CSCAPES Mission Research and development –Load balancing and parallelization toolkits for petascale computing –Automatic differentiation capabilities –Advanced sparse matrix methods Major software outlets (open source): –Zoltan and OpenAD/ADIC Training and outreach –Train researchers in CSC skills at pre-doctoral and post-doctoral levels –Organize workshops, tutorials and short courses in CSC –Collaborate with SciDAC SAPs and CETs, academia, and industry Accelerating the development and deployment of fundamental enabling technologies in high performance computing CSCAPES

Partitioning and Load Balancing Goal: assign data to processors to –minimize application runtime –maximize utilization of computing resources Metrics: –minimize processor idle time (balance work loads) –keep inter-processor communication costs low Impacts the performance of a wide range of simulations CSCAPES plans to extend Zoltan for petascale applications Adaptive Mesh Refinement Contact detection Particle Simulations x b A = Linear solvers & preconditioners CSCAPES

Combinatorics in Automatic Differentiation Automatic Differentiation computes analytic derivatives of functions specified by programs Derivative accumulation is posed as a graph problem –Represent a function using a directed acyclic graph –Vertices are intermediate variables, edge weights are partial derivatives –Compute sum of weights over all paths from independent to dependent variable(s) weight of a path P is product of weights of edges along P CSCAPES plans to –Develop algorithms to reduce flops by graph elimination –Find equivalent DAGs with fewest edges –Detect sparsity of derivative matrices, then use coloring to reduce cost –Differentiate parallel reduction operations by enumerating subsets from a distributed collection in parallel y x f a c t0 y d0 b a a expsin * * * CSCAPES

Graph Coloring for Computing Derivatives Sparsity exploitation leads to a variety of graph coloring problems Coloring also discovers concurrency in parallel computing Developed novel algorithms for several coloring problems Preliminary parallel versions developed for two coloring problems CSCAPES plans to –Extend coloring software and integrate with AD tools –Design petascale parallel coloring algorithms CSCAPES

Matching for Sparse Matrix Computations Graph matching has many applications in sparse matrix computations and graph partitioning Traditional matching algorithms compute optimal solutions in super- linear time and are difficult to parallelize Current research trends are toward linear time approximation algorithms and parallelization CSCAPES plans to develop petascale parallel matching algorithms based on approximation techniques CSCAPES

Performance Improvement via Data Reordering Irregular memory access patterns make performance sensitive to data and iteration orders Run-time reordering transformations schedule data accesses and iterations to maximize performance Preliminary work on reordering heuristics [Strout & Hovland, 2004] shows that hypergraph models outperform graph models CSCAPES plans to develop hypergraph-based runtime reordering transformations CSCAPES