Generating the set of candidate network edges to add includes phylogenetically inconsistent edges

[recursion-ninja]

Some of the edges generated connect to an ancestor in their path to one of the root nodes. This allows us to construct phylogenetically inconsistent networks when consuming the list of candidate network edges.

[recursion-ninja]

Properties that the candidate network edges should satisfy are:

• The new edge cannot go into an existing edge with source or target network node.

• Neither of the edges should be ancestral to one another:

  1. Collect the set of ancestral edges for the two edges we are considering.
  2. Perform set intersection of ancestral edge sets of the two edges.
  3. If the intersection is empty, there is no ancestral violation in adding an edge between the two edges.

• Nether of the two edges should be temporally inconsistent:

  1. Collect the set of network nodes descendant to each ancestor (except the root) of the target node.
  2. Collect the set of network nodes descendant to the source node.
  3. Perform set intersection of the sets.
  4. If the intersection is empty, there is no temporal inconsistency in adding an edge between the two edges.

[Boarders]

If we allow creating a new network node from a source edge to a target edge and the source edge contains a root node then the run time system gives a <> error during the scoring indicating that it has detected an infinite loop. For now I have disallowed this possibility from the candidate edges but this does rule out adding edges we may otherwise wish to have. It may be worth investigating why this is in a separate issue.

[recursion-ninja]

We should write a LaTeX document in doc/tex/ that describes the psuedocode of how to efficiently generate the set of candidate network edges.