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Improving the layout of splits networks
Philippe Gambette Daniel Huson
http//philippe.gambette.free.fr/Tuebingen
06/06/2005
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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
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Splits graphs
Every edge splits the tree into 2 parts
x2
x1
x6
x3
x5
x4
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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 ltgt tree
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Splits graphs
Incompatible splits
x1
x2
x6
x3
box
x4
x5
incompatible splits ltgt box
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Splits graphs
Circular splits
x1
x2
x6,x1
S
x2,x3,x4,x5
The split is circular
x6
x3
box
x4
x5
All the splits are circular gt planar graph
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Drawing planar splits graph equal angle algorithm
Splits graph are associated with their taxa
circle taxa displayed regularly around the
circle

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 Opening boxes 
Improving the layout of the graphs opening boxes
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 Opening boxes  from the taxa circle
Advantages - we dont have to consider all the
edges, just the splitsk operations instead of
k.n². - 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.
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Opening boxes  by moving the taxa
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 Opening boxes  by moving the taxa
Save a best position. Do the following loop n
times For each taxon, try to move it if its
better save it, try to move another taxon. if
its better thant the best, save as best. else
save it with a probability p20.gt nice results
for small graphs
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 Opening boxes  once the graph is drawn
The graph must remain planar Identify critical
angles for the split angle
Considering the only split itself, changing a0.
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 Opening boxes  once the graph is drawn
The graph must remain planar Identify critical
angles for the split angle.
Considering the only split itself, changing a0.
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 Opening boxes  once the graph is drawn
The graph must remain planar Identify critical
angles for the split angle.
Considering collisions in the graph.
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 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
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 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
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 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!
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 Opening boxes  once the graph is drawn
Danger area for our criteriaon its border, the
striker arrives exactly on the the defenders
line.
Equation of the border of the area
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 Opening boxes  once the graph is drawn
Danger area for our criteria, depending on the
angle of the defender
The case never happens after the equal angle
algorithm.
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Algorithm
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Results
Before the optimization
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Results
After 1 loop (10 secs on a 2.6GHz Pentium)
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Results
After 2 loops
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Results
After 3 loops
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Results
After 4 loops
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Results
After 5 loops
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Results
After 6 loops
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Results
After 7 loops
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Results
After 8 loops
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Results
After 9 loops
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Results
After 10 loops
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What about the names of the algorithms ???
Both algorithms box-opening
Algorithm 1 taxa, circular, before the
layout...
Algorithm 2 collisions, danger...