Balanced Graph Partition Refinement using the Graph p-Laplacian
Additional information
Authors
Type
Article in conference proceedings
Year
2018
Language
English
Abstract
A continuous formulation of the optimal 2-way graph partitioning based on the p-norm minimization of the graph Laplacian Rayleigh quotient is presented, which provides a sharp approximation to the balanced graph partitioning problem, the optimality of which is known to be NP-hard. The minimization is initialized from a cut provided by a state-of-the-art multilevel recursive bisection algorithm, and then a continuation approach reduces the p-norm from a 2-norm towards a 1-norm, employing for each value of p a feasibility-preserving steepest-descent method that converges on the p-Laplacian eigenvector. A filter favors iterates advancing towards minimum edgecut and partition load imbalance. The complexity of the suggested approach is linear in graph edges. The simplicity of the steepest-descent algorithm renders the overall approach highly scalable and efficient in parallel distributed architectures. Parallel implementation of recursive bisection on multi-core CPUs and GPUs are presented for large-scale graphs with up to 1.9 billion tetrahedra. The suggested approach exhibits improvements of up to 52.8% over METIS for graphs originating from triangular Delaunay meshes, 34.7% over METIS and 21.9% over KaHIP for power network graphs, 40.8% over METIS and 20.6% over KaHIP for sparse matrix graphs, and finally 93.2% over METIS for graphs emerging from social networks.
Conference proceedings
Proceedings of the ACM Platform for Advanced Scientific Computing Conference
Month
July
Publisher
ACM
Series
PASC’18
Meeting name
Platform for Advanced Scientific Computing Conference (PASC)
Meeting place
Basel
Meeting date
July 02 - 04, 2018
