ISIPhyNC - Class: binary time-consistent
Definition
A phylogenetic network is binary time-consistent if it is binary and it is time-consistent. Also called binary temporal networks. [reference]Bibliographic references on the Who is who in phylogenetic networks
Relationships with other phylogenetic network classes
Maximum subclasses
Minimum superclasses
Problems
Positive results proved for this class
-
No positive result found
Positive results deduced from superclasses
- Phylogenetic Network Isomorphism, positive result on binary: The phylogenetic network isomorphism problem can be solved in O(n4) time on binary networks. Simulations show that the algorithm is practical, with instances of 500 vertices solved in less than one tenth of a second. [reference]
Negative results proved for this class
- Tree Containment: NP-hard, reduction from Tree Containment on binary networks. [reference] (Theorem 3)
Negative results deduced from subclasses
-
No negative result could be deduced from subclasses.
Properties
Properties proved for this class
-
No property found
Properties deduced from superclasses
-
No property could be deduced from superclasses.
Properties deduced from subclasses
-
No property could be deduced from subclasses.
Examples of networks
In this class
proved directly:
network #7 : Here is a time-consistent labeling t:
- t(r)=0
- t(a)=t(b)=t(e)=1
- t(c)=t(d)=t(f)=t(1)=2
- t(2)=t(3)=t(4)=3
network #3 : Here is a time-consistent labeling t:
- t(r)=0
- t(a)=t(f)=1
- t(b)=t(c)=t(d)=t(e)=t(g)=t(h)=t(i)=2
- t(1)=t(2)=t(3)=t(4)=t(5)=3
network #2 : Here is a time-consistent labeling t:
- t(r)=0
- t(a)=1
- t(b)=2
- t(c)=t(d)=t(e)=t(f)=t(g)=t(h)=t(i)=3
- t(1)=t(2)=t(3)=t(4)=t(5)=4
network #8 : Here is a time-consistent labeling t:
- t(r)=0
- t(a)=1
- t(d)=t(i)=2
- t(g)=t(5)=3
- t(b)=t(e)=t(h)=4
- t(c)=t(f)=t(1)=t(4)=5
- t(2)=t(3)=6
network #23 : Here is a time-consistent labeling t:
- t(r)=0
- t(a)=t(g)=1
- t(b)=t(c)=t(d)=t(e)=t(f)=t(h)=t(i)=t(j)=2
- t(1)=t(2)=t(3)=t(4)=3
Deduced from class inclusions: no network found in this class using class inclusions
Not in this class
Proved directly:
network #5 : The redundant arc from r to c makes it impossible to build a time-consistent labeling of the vertices.
network #6 : The redundant arc from r to b makes it impossible to build a time-consistent labeling of the vertices.
network #22 : If the network is time-consistent, then there would exist a time-consistent labeling t. As a and f are b's parents, t(a)=t(b)=t(f). As c and e are d's parents, t(c)=t(d)=t(e). However, t(f)>t(e) and t(c)>t(a).
network #1 : The redundant arc from f to a makes it impossible to build a time-consistent labeling of the vertices.
network #10 : The redundant arc from a to c makes it impossible to build a time-consistent labeling of the vertices.
network #4 : The redundant arc from b to e makes it impossible to build a time-consistent labeling of the vertices.
Deduced from class inclusions: no network found outside this class using class inclusions
About this website
This website was programmed and is maintained by Philippe Gambette. It was started during the internship of Maxime Morgado at LIGM, in June-July 2015, and also contains contributions made from Narges Tavassoli from November 2016 to January 2017.
Please contact Philippe Gambette if you have any suggestions about this website, especially about problems, properties, results or subclasses to add.
How to cite
P. Gambette, M. Morgado, N. Tavassoli & M. Weller (2018) ISIPhyNC, an Information System on Inclusions of Phylogenetic Network Classes, manuscript in preparation.
Database content
73 classes of phylogenetic networks including 35 classes of binary phylogenetic networks (defined in a total of 20 bibliographic references), 51 inclusion relationships proved directly between classes (including some found in a total of 9 bibliographic references), 24 networks (68 memberships to a class, 56 non-memberships to a class), 3 problems considered, 3 properties considered, 37 theorems proved directly (including some found in a total of 17 bibliographic references) including 26 positive results (which can be extended to subclasses) and 11 negative results (which can be extended to superclasses).
