Table 1 Each counter gives the number of triplets shared between a query tree T (or a rerooting of T; 2nd column) that are anchored at a particular node of T (e.g., u; 3rd column) and a component X of the HDT (4th column)
From: Median quartet tree search algorithms using optimal subtree prune and regraft
| Â | Rerooting T at | Shared triplets anchored at | Under HDT component |
|---|---|---|---|
Counters of a node u of T | |||
\(\tau _{u}^i\) | no rerooting | node u | \(\mathfrak {R}\) |
\(\tau _{u}^r\) | \((u^{\uparrow },u)\) | new root of \(T^\oplus _{u}\) | \(\mathfrak {R}\) |
\(\tau _u^o\) | \((u^{\uparrow },u)\) | new sister to u (old \(u^{\uparrow }\)) | \(\mathfrak {R}\) |
Counters of a component X of the HDT | |||
\(\pi ^X_0\) | no rerooting | node u | X |
\(\rho ^X\) | \((u^{\uparrow },u)\) | new root of \(T^\oplus _{u}\) | X |
\(\pi ^X_j\) | \((u,v_j)\) | new sister to \(v_j\) (old u) | X |