Graph partitioning and disturbed diffusion

The NP-hard graph partitioning problem is an important subtask in load balancing and many other applications. It requires the division of a graph’s vertex set into P equally sized subsets such that some objective function is optimized. State-of-the-art libraries addressing this problem show several deficiencies: they are hard to parallelize, focus on small edge-cuts instead of few boundary vertices, and often produce disconnected partitions. This work introduces our novel graph partitioning and repartitioning heuristic BubbleFOS/C. In contrast to other libraries, Bubble-FOS/C does not try to minimize the edgecut explicitly, but focuses instead implicitly on good partition shapes. The shapes are optimized by diffusion processes that are embedded into an iterative framework. This approach incorporates a high degree of parallelism. Besides describing the evolution process that led to the new diffusion scheme FOS/C used by Bubble-FOS/C, we reveal some of FOS/C’s properties and propose a number of enhancements for a fast and reliable implementation. Our experiments, in which we compare sequential and parallel Bubble-FOS/C implementations to the state-of-the-art libraries Metis and Jostle, reveal that our new heuristic generates high-quality solutions.