Scaling betweenness centrality using communication-efficient sparse matrix multiplication

TL;DR

This paper introduces MFBC, a communication-efficient sparse matrix multiplication-based algorithm for betweenness centrality that outperforms existing methods and scales well across various graph densities.

Contribution

The paper presents MFBC, a novel, scalable, and communication-efficient algorithm for betweenness centrality using monoids for weighted graphs, with automatic data decomposition optimization.

Findings

MFBC reduces communication by a factor of p^{1/3} compared to previous methods.

MFBC outperforms CombBLAS by up to 8x in speed.

MFBC scales effectively for both sparse and dense graphs.

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 $p^{1/3}$ 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.