SLIDE 1
1
2 - 1
Drawing Tree-Based Phylogenetic Networks with Minimum Number of - - PowerPoint PPT Presentation
Drawing Tree-Based Phylogenetic Networks with Minimum Number of - - PowerPoint PPT Presentation
1 Drawing Tree-Based Phylogenetic Networks with Minimum Number of Crossings Jonathan Klawitter Peter Stumpf GD 2020 2 - 1 Phylogenetic networks T 1 2 3 4 5 2 - 2 Phylogenetic networks T N 1 2 3 4 5 1 2 3 4 5 2 - 3
SLIDE 2
SLIDE 3
2 - 2
Phylogenetic networks
T 1 2 3 4 5 N 1 2 3 4 5
SLIDE 4
2 - 3
Phylogenetic networks
T 1 2 3 4 5 N 1 2 3 4 5 N 1 2 3 4 5
SLIDE 5
2 - 4
Phylogenetic networks
T 1 2 3 4 5 N 1 2 3 4 5 N 1 2 3 4 5 T′ 1 2 3 4 5
SLIDE 6
3 - 1
Kumar et al. “The evolutionary history of bears is characterized by gene flow across species”
SLIDE 7
3 - 2
Richards et al. “Phylogenomic Analysis Demonstrates a Pattern of Rare and Ancient Horizontal Gene Transfer between Plants and Fungi” Kumar et al. “The evolutionary history of bears is characterized by gene flow across species”
SLIDE 8
3 - 3
Richards et al. “Phylogenomic Analysis Demonstrates a Pattern of Rare and Ancient Horizontal Gene Transfer between Plants and Fungi” Kumar et al. “The evolutionary history of bears is characterized by gene flow across species” Vaughan et al. “Inferring Ancestral Recombination Graphs from Bacterial Genomic Data”
SLIDE 9
4 - 1
Drawing styles
SLIDE 10
4 - 2
Drawing styles
SLIDE 11
4 - 3
Drawing styles
SLIDE 12
4 - 4
Drawing styles
SLIDE 13
4 - 5
Drawing styles
SLIDE 14
4 - 6
Drawing styles
snake style
SLIDE 15
4 - 7
Drawing styles
snake style
SLIDE 16
4 - 8
Drawing styles
snake style ear style
SLIDE 17
4 - 9
Drawing styles
snake style ear style horizontal style
SLIDE 18
4 - 10
Drawing styles
snake style ear style horizontal style
SLIDE 19
4 - 11
Drawing styles
snake style ear style horizontal style
SLIDE 20
5 - 1
Let N be a tree-based network on n leaves and k reticulation edges. A crossing-minimal ear-style drawing
- f N can be computed in O(nk) time.
SLIDE 21
5 - 2
Let N be a tree-based network on n leaves and k reticulation edges. A crossing-minimal ear-style drawing
- f N can be computed in O(nk) time.
SLIDE 22
5 - 3
Let N be a tree-based network on n leaves and k reticulation edges. A crossing-minimal ear-style drawing
- f N can be computed in O(nk) time.
SLIDE 23
5 - 4
Let N be a tree-based network on n leaves and k reticulation edges. A crossing-minimal ear-style drawing
- f N can be computed in O(nk) time.
SLIDE 24
5 - 5
Let N be a tree-based network on n leaves and k reticulation edges. A crossing-minimal ear-style drawing
- f N can be computed in O(nk) time.
SLIDE 25
5 - 6
Let N be a tree-based network on n leaves and k reticulation edges. A crossing-minimal ear-style drawing
- f N can be computed in O(nk) time.
SLIDE 26
6 - 1
Ear-style algorithm
SLIDE 27
6 - 2
Ear-style algorithm 0 0 0 0 0 0 0 0
SLIDE 28
6 - 3
Ear-style algorithm 0 0 0 0 0 0 0 0
SLIDE 29
6 - 4
Ear-style algorithm 0 0 0 0 0 0 0 0
SLIDE 30
6 - 5
Ear-style algorithm 0 1 0 0 0 0 0 0
SLIDE 31
6 - 6
Ear-style algorithm 0 1 0 2 2
SLIDE 32
6 - 7
Ear-style algorithm 1 1 0 0 2 0 2 3
SLIDE 33
6 - 8
Ear-style algorithm 1 1 0 0 2 0 2 3
SLIDE 34
6 - 9
Ear-style algorithm 0 1 2 1 3 3
SLIDE 35
6 - 10
Ear-style algorithm 0 1 2 1 3 3
SLIDE 36
6 - 11
Ear-style algorithm 1 0 2 1 3 3
SLIDE 37
6 - 12
Ear-style algorithm 2 1 3 3
SLIDE 38
6 - 13
Ear-style algorithm 2 1 3 3
SLIDE 39
6 - 14
Ear-style algorithm 3 4
SLIDE 40
6 - 15
Ear-style algorithm 3 4
SLIDE 41
6 - 16
Ear-style algorithm 4 3
SLIDE 42
6 - 17
Ear-style algorithm
SLIDE 43
7 - 1
The Crossing Minimisation problem for horizontal-style drawings of tree-based networks is NP-complete.
SLIDE 44
7 - 2
The Crossing Minimisation problem for horizontal-style drawings of tree-based networks is NP-complete. G MaxCut
SLIDE 45
8 - 1
Horizontal style NP-reduction
u v w g e f G
SLIDE 46
8 - 2
Horizontal style NP-reduction
u v w g e f G ue ve Ne e′
SLIDE 47
8 - 3
Horizontal style NP-reduction
u v w g e f G ue ve Ne e′ ug wg Ng g′
SLIDE 48
8 - 4
Horizontal style NP-reduction
u v w g e f G ue ve Ne e′ ug wg Ng g′ v f w f f ′ Nf
SLIDE 49
8 - 5
Horizontal style NP-reduction
u v w g e f G ue ve Ne e′ ug wg Ng g′ v f w f f ′ Nf
SLIDE 50
8 - 6
Horizontal style NP-reduction
u v w g e f G ue ve Ne e′ ug wg Ng g′ v f w f f ′ ue ug Nf
SLIDE 51
8 - 7
Horizontal style NP-reduction
u v w g e f G ue ve Ne e′ ug wg Ng g′ v f w f f ′ ue ug u⋆ Nf
SLIDE 52
8 - 8
Horizontal style NP-reduction
u v w g e f G ue ve Ne e′ ug wg Ng g′ v f w f f ′ ue ug u⋆ Nf
SLIDE 53
8 - 9
Horizontal style NP-reduction
u v w g e f G ue ve Ne e′ ug wg Ng g′ v f w f f ′ ue ug u⋆ Nf
SLIDE 54
8 - 10
Horizontal style NP-reduction
u v w g e f G
SLIDE 55
8 - 11
Horizontal style NP-reduction
u v w g e f G
SLIDE 56
8 - 12
Horizontal style NP-reduction
u v w g e f G
SLIDE 57
8 - 13
Horizontal style NP-reduction
u v w g e f G
SLIDE 58
8 - 14
Horizontal style NP-reduction
u v w g e f G
SLIDE 59
8 - 15
Horizontal style NP-reduction
u v w g e f G
SLIDE 60
9 - 1
Let N be a tree-based network on n leaves and k reticulation edges. A crossing-minimal snake-style drawing
- f N can be computed in O(2knk) time.
SLIDE 61
9 - 2
Let N be a tree-based network on n leaves and k reticulation edges. A crossing-minimal snake-style drawing
- f N can be computed in O(2knk) time.
SLIDE 62
9 - 3
Let N be a tree-based network on n leaves and k reticulation edges. A crossing-minimal snake-style drawing
- f N can be computed in O(2knk) time.
SLIDE 63
10
Let N be a tree-based network on n leaves and k reticulation edges. A crossing-minimal ear-style drawing
- f N can be computed in O(nk) time.
Let N be a tree-based network on n leaves and k reticulation edges. A crossing-minimal snake-style drawing
- f N can be computed in O(2knk) time.