A Parallel Hill-Climbing Refinement Algorithm for Graph Partitioning

Graph partitioning is important in distributing workloads on parallel compute systems, computing sparse matrix re-orderings, and designing VLSI circuits. Refinement algorithms are used to improve existing partitionings, and are essential for obtaining high-quality partitionings. Existing parallel refinement algorithms either extract concurrency by sacrificing in terms of quality, or preserve quality by restricting concurrency. In this work we present a new shared-memory parallel algorithm for refining an existing k-way partitioning that can break out of local minima and produce high-quality partitionings. This allows our algorithm to scale well in terms of the number of processing cores and produce clusterings of quality equal to serial algorithms. Our algorithm achieves speedups of 5.7-16.7x using 24 cores, while exhibiting only 0.52% higher edgecuts than when run serially. This is 6.3x faster and 1.9% better quality than other parallel refinement algorithms which can break out of local minima.