@inproceedings{5c96692f2f3e41d5be23a05afed9d970,

title = "Mathematical foundations of the GraphBLAS",

abstract = "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 paper 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. Performance measurements of prototype GraphBLAS implementations indicate that the overhead is low.",

author = "Jeremy Kepner and Peter Aaltonen and David Bader and Aydin Buluc and Franz Franchetti and John Gilbert and Dylan Hutchison and Manoj Kumar and Andrew Lumsdaine and Henning Meyerhenke and Scott Mcmillan and Carl Yang and Owens, {John D.} and Marcin Zalewski and Timothy Mattson and Jose Moreira",

note = "Publisher Copyright: {\textcopyright} 2016 IEEE.; 2016 IEEE High Performance Extreme Computing Conference, HPEC 2016 ; Conference date: 13-09-2016 Through 15-09-2016",

year = "2016",

month = nov,

day = "28",

doi = "10.1109/HPEC.2016.7761646",

language = "English (US)",

series = "2016 IEEE High Performance Extreme Computing Conference, HPEC 2016",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

booktitle = "2016 IEEE High Performance Extreme Computing Conference, HPEC 2016",

address = "United States",

}