Table 1
Q-RAND(S, Q):
1.
 Randomly select a quartet topology in Q as the initial phylogeny T;
2.
 Delete the four taxa of T from the taxon set S;
3.
 Randomly select a taxon s from S;
4.
 Locate a separator v of T;
5.
 Randomly select a taxon from each sub-phylogeny of T - {v}, say sa, sb, and sc;
6.
 Decide which sub-phylogeny of T - {v} taxon s should be inserted into based on the quartet topology for {sa, sb, sc, s};
7.
 If the located sub-phylogeny has only one edge,
7.1.
      Insert 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 4;
9.
 Delete taxon s from S;
10.
 If S is not empty,
10.1.
      Go back to Step 3;
11.
 Else,
11.1.
      Output the phylogeny T.

Wu et al. Algorithms for Molecular Biology 2008 3:1   doi:10.1186/1748-7188-3-1