Scaling betweenness centrality using communication-efficient sparse matrix multiplication

Betweenness centrality (BC) is a crucial graph problem that measures the significance of a vertex by the number of shortest paths leading through it. We propose Maximal Frontier Betweenness Centrality (MFBC): a succinct BC algorithm based on novel sparse matrix multiplication routines that performs...

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Published in:International Conference for High Performance Computing, Networking, Storage and Analysis (Online) pp. 1 - 14
Main Authors: Solomonik, Edgar, Besta, Maciej, Vella, Flavio, Hoefler, Torsten
Format: Conference Proceeding
Language:English
Published: New York, NY, USA ACM 12.11.2017
Series:ACM Conferences
Subjects:
Betweenness centrality
communication cost
Computing methodologies > Parallel computing methodologies > Parallel algorithms > Massively parallel algorithms
Computing methodologies > Symbolic and algebraic manipulation > Symbolic and algebraic algorithms > Algebraic algorithms
Design methodology
Distributed databases
High performance computing
Mathematics of computing > Mathematical software > Mathematical software performance
parallel algorithm
Program processors
Software algorithms
Software performance
sparse matrix multiplication
Tensors
Theory of computation > Design and analysis of algorithms > Parallel algorithms > Massively parallel algorithms
communication cost
sparse matrix multiplication
betweenness centrality
parallel algorithm
ISBN:9781450351140, 145035114X
ISSN:2167-4337
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Abstract Betweenness centrality (BC) is a crucial graph problem that measures the significance of a vertex by the number of shortest paths leading through it. We propose Maximal Frontier Betweenness Centrality (MFBC): a succinct BC algorithm based on novel sparse matrix multiplication routines that performs a factor of p1/3 less communication on p processors than the best known alternatives, for graphs with n vertices and average degree k = n/p2/3. We formulate, implement, and prove the correctness of MFBC for weighted graphs by leveraging monoids instead of semirings, which enables a surprisingly succinct formulation. MFBC scales well for both extremely sparse and relatively dense graphs. It automatically searches a space of distributed data decompositions and sparse matrix multiplication algorithms for the most advantageous configuration. The MFBC implementation outperforms the well-known CombBLAS library by up to 8x and shows more robust performance. Our design methodology is readily extensible to other graph problems.
AbstractList Betweenness centrality (BC) is a crucial graph problem that measures the significance of a vertex by the number of shortest paths leading through it. We propose Maximal Frontier Betweenness Centrality (MFBC): a succinct BC algorithm based on novel sparse matrix multiplication routines that performs a factor of p1/3 less communication on p processors than the best known alternatives, for graphs with n vertices and average degree k = n/p2/3. We formulate, implement, and prove the correctness of MFBC for weighted graphs by leveraging monoids instead of semirings, which enables a surprisingly succinct formulation. MFBC scales well for both extremely sparse and relatively dense graphs. It automatically searches a space of distributed data decompositions and sparse matrix multiplication algorithms for the most advantageous configuration. The MFBC implementation outperforms the well-known CombBLAS library by up to 8x and shows more robust performance. Our design methodology is readily extensible to other graph problems.
Betweenness centrality (BC) is a crucial graph problem that measures the significance of a vertex by the number of shortest paths leading through it. We propose Maximal Frontier Betweenness Centrality (MFBC): a succinct BC algorithm based on novel sparse matrix multiplication routines that performs a factor of p^{1/3} less communication on p processors than the best known alternatives, for graphs with n vertices and average degree k=n/p^{2/3}. We formulate, implement, and prove the correctness of MFBC for weighted graphs by leveraging monoids instead of semirings, which enables a surprisingly succinct formulation. MFBC scales well for both extremely sparse and relatively dense graphs. It automatically searches a space of distributed data decompositions and sparse matrix multiplication algorithms for the most advantageous configuration. The MFBC implementation outperforms the well-known CombBLAS library by up to 8x and shows more robust performance. Our design methodology is readily extensible to other graph problems. CCS CONCEPTS * Theory of computation → Massively parallel algorithms; * Mathematics of computing → Mathematical software performance; * Computing methodologies → Algebraic algorithms; Massively parallel algorithms;
Author Vella, Flavio
Solomonik, Edgar
Besta, Maciej
Hoefler, Torsten
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Keywords communication cost
sparse matrix multiplication
betweenness centrality
parallel algorithm
Language English
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Snippet Betweenness centrality (BC) is a crucial graph problem that measures the significance of a vertex by the number of shortest paths leading through it. We...
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SubjectTerms Betweenness centrality
communication cost
Computing methodologies -- Parallel computing methodologies -- Parallel algorithms -- Massively parallel algorithms
Computing methodologies -- Symbolic and algebraic manipulation -- Symbolic and algebraic algorithms -- Algebraic algorithms
Design methodology
Distributed databases
High performance computing
Mathematics of computing -- Mathematical software -- Mathematical software performance
parallel algorithm
Program processors
Software algorithms
Software performance
sparse matrix multiplication
Tensors
Theory of computation -- Design and analysis of algorithms -- Parallel algorithms -- Massively parallel algorithms
Title Scaling betweenness centrality using communication-efficient sparse matrix multiplication
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