
20.5. PHYLOGENETIC TREES 641
δ ((v, w)). This should sup port the algorithm to draw edges with their desired length, but
raises the r u nn in g time to O(|V |log |V |), however. Since even this cannot guar antee exact
lengths, the ed ges are colored, i.e., blue color means too sh ort and red color too large, such
that the color saturation reflects the multiplicative failure.
((x(v), y(v)) ←
(x(u), y(u))
δ ((u, v))
+
X
w∈W
(x(w), y(w))
δ ((v, w)) · |W |
(20.10)
Input: T = (V, E, δ) with δ(e) > 0 for all edges e
Output: Coord in ates x, y : V → R for the nodes
Data: Coefficients c: V → R, offsets d : V → R
2
, and edge weights s : E → R
for each v ∈ V if deg(v) =