Table 3 :

M-VOTE(S, Q, p):

1.

Search for a 5-subset compatible with Q;

2.

If successful

2.1

   Let the corresponding phylogeny be the current phylogeny T;

2.2

   Delete the 5 taxa of T from the taxon set S;

3.

Else

3.1

   Randomly select a quartet topology in Q as the current phylogeny T;

3.2

   Delete the four taxa of T from the taxon set S;

4.

Randomly select a taxon s from S;

5.

Locate a separator v of T;

6.

Decide which sub-phylogeny of T - {v} taxon s should be inserted into based on the votes;

7.

If the located sub-phylogeny has only one edge,

7.1.

   Insert taxon s on that edge and let the new phylogeny be T;

8.

Else,

8.1.

   Merge the other two sub-phylogenies as a super taxon (which replaces v);

8.2.

   Let the located sub-phylogeny with the super taxon be the new current phylogeny T;

8.3.

   Go back to Step 5;

9.

Delete taxon s from S;

10.

If S is not empty,

10.1.

   Go back to Step 4;

11.

Else,

11.1.

   Output the phylogeny T.