A Diffusion Process for Graph Partitioning: Its Solutions and Their Improvement

We present a diffusion process on graphs for k-way partitioning. In this approach, various species propagate on the graph that cancel each other out, and every partition is represented by one species of the converged solution. The vertices and edges of the graph are reservoirs and resistances, respectively, and source terms are placed on the vertices. A distribution of these source terms on the graph is suggested and the resulting k-way partitioning of the diffusion process for basic graphs discussed. We present reference examples in which complex graphs are recursively bi-partitioned with a diffusion step and a subsequent Kernighan-Lin improvement step. For comparison the graphs are also partitioned with multilevel methods and a subsequent Kernighan-Lin improvement. For certain graphs the diffusion approach produces the best partitions.

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