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

2. The problem 1101011001111000000000000000000 1111111111111000000000000000000 1111111111111111010000000000000 1111111111111111110000000000000 1111111111111111110000000000000 1111111001011101010000000000000 1111111110101001000000000000000 1111110011110011010000000000000 1111111111111110010000000000000 1111111111111011001111110111110 0000000000000000000111100111110 0000000000000000001111111111110 0000000000000000000101111000000

4. 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)

5. 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

6. Lower bounds

7. 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?