A Parallel Framework for Approximate Max-Dicut in Partitionable Graphs

Computing a maximum cut in undirected and weighted graphs is a well studied problem and has many practical solutions that also scale well in shared memory (despite its NP-completeness). For its counterpart in directed graphs, however, we are not aware of practical solutions that also utilize parallelism. We engineer a framework that computes a high quality approximate cut in directed and weighted graphs by using a graph partitioning approach. The general idea is to partition a graph into k subgraphs using a parallel partitioning algorithm of our choice (the first ingredient of our framework). Then, for each subgraph in parallel, we compute a cut using any polynomial time approximation algorithm (the second ingredient). In a final step, we merge the locally computed solutions using a high-quality or exact parallel Max-Dicut algorithm (the third ingredient). On graphs that can be partitioned well, the quality of the computed cut is significantly better than the best cut achieved by any linear time algorithm. This is particularly relevant for large graphs, where linear time algorithms used to be the only feasible option.