Mathematical foundations of the GraphBLAS

Journal Article · Thu Dec 01 00:00:00 EST 2016 · 2016 IEEE High Performance Extreme Computing Conference, HPEC 2016

DOI:https://doi.org/10.1109/HPEC.2016.7761646· OSTI ID:1379592

Kepner, Jeremy ^[1]; Aaltonen, Peter ^[2]; Bader, David ^[3]; Buluc, Aydin ^[4]; Franchetti, Franz ^[5]; Gilbert, John ^[6]; Hutchison, Dylan ^[7]; Kumar, Manoj ^[8]; Lumsdaine, Andrew ^[2]; Meyerhenke, Henning ^[9]; McMillan, Scott ^[10]; Yang, Carl ^[8]; Owens, John D. ^[11]; Zalewski, Marcin ^[11]; Mattson, Timothy ^[2]; Moreira, Jose ^[12]

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1. MIT Lincoln Lab. Supercomputing Center, Lexington, MA (United States)
2. Indiana Univ., Bloomington, IN (United States)
3. Georgia Inst. of Technology, Atlanta, GA (United States)
4. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
5. Carnegie Mellon Univ., Pittsburgh, PA (United States)
6. Univ. of California, Santa Barbara, CA (United States)
7. Univ. of Washington, Seattle, WA (United States)
8. IBM, Armonk, NY (United States)
9. Karlsruhe Inst. of Technology (KIT) (Germany)
10. CMU Software Engineering Inst., Pittsburgh, PA (United States)
11. Univ. of California, Davis, CA (United States)
12. Intel, Santa Clara, CA (United States)

The GraphBLAS standard (GraphBlas.org) is being developed to bring the potential of matrix-based graph algorithms to the broadest possible audience. Mathematically, the GraphBLAS defines a core set of matrix-based graph operations that can be used to implement a wide class of graph algorithms in a wide range of programming environments. This study provides an introduction to the mathematics of the GraphBLAS. Graphs represent connections between vertices with edges. Matrices can represent a wide range of graphs using adjacency matrices or incidence matrices. Adjacency matrices are often easier to analyze while incidence matrices are often better for representing data. Fortunately, the two are easily connected by matrix multiplication. A key feature of matrix mathematics is that a very small number of matrix operations can be used to manipulate a very wide range of graphs. This composability of a small number of operations is the foundation of the GraphBLAS. A standard such as the GraphBLAS can only be effective if it has low performance overhead. Finally, performance measurements of prototype GraphBLAS implementations indicate that the overhead is low.

• Research Organization: Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); National Science Foundation (NSF); USDOD
• DOE Contract Number: AC02-05CH11231; DMS-1312831; FA8721-05-C-0003
• OSTI ID: 1379592
• Journal Information: 2016 IEEE High Performance Extreme Computing Conference, HPEC 2016, Journal Name: 2016 IEEE High Performance Extreme Computing Conference, HPEC 2016
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
matrices
sparse matrices
finite element analysis
standards
additives
programming environments
graph theory
mathematics computing
matrix algebra