Confluent Drawings of Bipartite/Layered Graphs Ulrik, Riko, Stephen, Titto, Nina.

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Presentation transcript:

Confluent Drawings of Bipartite/Layered Graphs Ulrik, Riko, Stephen, Titto, Nina

The problem

Bipartite Bandwidth Given adjacency matrix M, minimize [max(i-j)-min(i-j)] over all edges (i,j). The problem can be shifted, i.e., we allow only adjacency matrices where for all edges (i,j) i>j. (E.g., by introducing additional columns). Now, the objective reduces to: min max(i-j)

Results Find optimal adjacency matrix: reduction from bandwidth -> NP-hard, not approximable by a constant factor; Fix one side, optimize the other: in P by solving perfect matching or bottleneck matching; Immediately allows sequential heuristic in Sugiyama style

Lower bounds

Open Problems What if we optimize the total ink use? Practical approach for real-world bipartite graphs? – Very dense To do: – Implement, test on hierarchically layered graphs – Make tests with users about visual appeal?