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Improving the layout of splits networks

Improving the layout of splits networks. Philippe Gambette & Daniel Huson. http://philippe.gambette.free.fr/Tuebingen/indexENG.htm. 06/06/2005. Caution! Some parts of this presentation have become Outdated ! due to later results. Outline.  Phylogenetic networks and splits graphs

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Improving the layout of splits networks

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  1. Improving the layout of splits networks Philippe Gambette & Daniel Huson http://philippe.gambette.free.fr/Tuebingen/indexENG.htm 06/06/2005 Caution! Some parts of this presentation have become Outdated ! due to later results

  2. Outline  Phylogenetic networks and splits graphs  Drawing planar phylogenetic networks  A strategy to open the boxes of small graphs  Another strategy to open the boxes

  3. Splits graphs {x6,x1,x2} S = {x3,x4,x5} Partition of the set of taxa A splits graph codes for a set of splits. For a tree: every edge splits the tree into 2 parts : x2 x1 x6 x3 x5 x4

  4. Splits graphs Compatible splits: x1 x2 x6 x3 {x6,x1,x2} {x1,x2} S = S’ = {x3,x4,x5} {x3,x4,x5,x6} x5 x4 all the splits are pairwise compatibletree

  5. Splits graphs {x6,x1} S = {x2,x3,x4,x5} {x1,x2} S’ = {x3,x4,x5,x6} Incompatible splits: x1 x2 x6 x3 box x4 x5 a pair of incompatible splits box

  6. Splits graphs Circular split: x1 x2 {x6,x1} S = {x2,x3,x4,x5} The split is circular x6 x3 box x4 x5 All the splits are circularouter-planar graph

  7. Drawing planar splits graph: equal angle algorithm Splits graph are associated with their taxa circle:the taxa are displayed regularly around the circle. =

  8. « Opening boxes » The weight of the edges is fixed Improving the layout of the graphs: opening boxes.

  9. « Opening boxes » from the taxa circle Advantages :- we don’t have to consider all the edges, just the splits:O(k) operations instead of O(n+k²).- we have a criteria for the graph to remain planar:keep the circular order of the taxa.Disadvantage :- there is not a lot of space aroundthe taxa circle.- the criteria of keeping the circularorder is not necessary.

  10. « Opening boxes » by moving the taxa

  11. « Opening boxes » by moving the taxa Store a best position. Do the following loop n times:For each taxon, try to move it : if it’s better : save it, try to move another taxon. if it’s better than the best, store as best. else : save it with a probability p=20%.  nice results for small graphs

  12. « Opening boxes » once the graph is drawn The graph must remain planar:Identify critical angles for the split angle. Considering only the split itself, changing a0:

  13. « Opening boxes » once the graph is drawn The graph must remain planar:Identify critical angles for the split angle. Considering only the split itself, changing a0: Outdated !

  14. « Opening boxes » once the graph is drawn The graph must remain planar:Identify critical angles for the split angle. Considering collisions in the graph.

  15. « Opening boxes » once the graph is drawn The graph must remain planar:Identify critical angles for the split angle. Identifying a defender and a striker: 4 extreme nodes

  16. « Opening boxes » once the graph is drawn The graph must remain planar:Identify critical angles for the split angle. Identifying a defender and a striker: 4 extreme nodes

  17. « Opening boxes » once the graph is drawn The graph must remain planar:Identify critical angles for the split angle. new angle E’’ is the new striker!

  18. « Opening boxes » once the graph is drawn Danger area for our criteria:on its border, the striker arrives exactly on the the defender’s line. Equation of the border of the area:

  19. « Opening boxes » once the graph is drawn Danger area for our criteria, depending on the angle of the defender: Those cases rarely happen.

  20. « Opening boxes » once the graph is drawn An example: Those cases rarely happen.

  21. Algorithm Do the following loop n times: For each split: If the total area of the boxes is not improved, break.

  22. Results Evolution of the total area of the boxes 1,5 1,4 1,3 Vig Penny 1,2 Bad Opt Boxes 1,1 Hard 1 Chainletters Outdated ! Mammals 0,9 Rubber 0,8 Primates 0,7 Algae Bees 0,6 0,5 0,4 0,3 0,2 0,1 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

  23. Results Improvement of the total area compared with the best area 0,75 0,70 0,65 Vig Penny 0,60 Bad Opt Boxes 0,55 Hard 0,50 Chainletters Outdated ! 0,45 Mammals 0,40 Rubber Primates 0,35 Algae 0,30 Bees 0,25 0,20 0,15 0,10 0,05 0,00 -0,05 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

  24. Results Before the optimization

  25. Results After 1 loop (10 secs on a 2.6GHz Pentium)

  26. Results After 2 loops

  27. Results After 3 loops

  28. Results After 4 loops

  29. Results After 5 loops

  30. Results After 6 loops

  31. Results After 7 loops

  32. Results After 8 loops

  33. Results After 9 loops

  34. Results After 10 loops

  35. What about the names of the algorithms ??? Both algorithms : box-opening Algorithm 1 : taxa, circular, before the layout…  optimized angle algorithm. Algorithm 2 : collisions, danger...

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