  In this paper, we study the maximum matching problem in RDV graphs, i.e.,
graphs that are vertex-intersection graphs of downward paths in a rooted tree.
We show that this problem can be reduced to a problem of testing (repeatedly)
whether a vertical segment intersects one of a dynamically changing set of
horizontal segments, which in turn reduces to an orthogonal ray shooting query.
Using a suitable data structure, we can therefore find a maximum matching in
$O(n\log n)$ time (presuming a linear-sized representation of the graph is
given), i.e., without even looking at all edges.
