Crossing Reduction of Sankey Diagram with Barycentre Ordering via Markov Chain

Abstract: Sankey diagram is popular for analyzing primary flows in network data. However, the growing complexity of data and hence crossings in the diagram begin to reduce its readability. In this work, we studied the NP-hard weighted crossing reduction problem of the Sankey diagram with both the common parallel form and the circular form. We expect to obtain an ordering of entities that reduces weighted crossings of links. We proposed a two-staged heuristic method based on the idea of barycentre ordering and used Markov chain to formulate the recursive process of obtaining such ordering. In the experiments, our method achieved 300.89 weighted crossings, compared with the optimum 278.68 from an integer linear programming method. Also, we obtained much less weighted crossings (87.855) than the state-of-art heuristic method (146.77). We also conducted a robust test which provided evidence that our method performed consistently against the change of complexity in the dataset.