Combinatorial Scientific Computing and Petascale Simulation (CSCAPES)

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Combinatorial Scientific Computing and Petascale
Simulation (CSCAPES)

• A SciDAC Institute Funded by DOEs
• Office of Science

www.cscapes.org

• 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)

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CSCAPES Mission
CSCAPES

• 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
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Partitioning and Load Balancing
CSCAPES

• 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

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Combinatorics in Automatic Differentiation
CSCAPES
f

• 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

a
c

a
b
y

exp
sin
t0
d0
a
y
x

• 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

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Graph Coloring for Computing Derivatives
CSCAPES

• 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

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Matching for Sparse Matrix Computations
CSCAPES

• 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

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Performance Improvement via Data Reordering
CSCAPES

• 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