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Parallel Combinatorial BLAS and Applications
in Graph Computations
Aydın
Buluç
John R. Gilbert
University of California, Santa Barbara
Adapted from talks at SIAM conferences

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By analogy to
numerical
linear algebra,
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What would the
combinatorial
BLAS look like?
Primitives for Graph Computations
BLAS 3
BLAS 2
BLAS 1
BLAS 3 (n-by-n matrix-matrix multiply)
BLAS 2 (n-by-n matrix-vector multiply)
BLAS 1 (sum of scaled n-vectors)
Peak

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Real-World Graphs
Properties:
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Huge (billions of vertices/edges)
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Very sparse (typically m = O(n))
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Scale-free [maybe]
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Community structure [maybe]
Examples:
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World-wide web
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Science citation graphs
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Online social networks

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