  We consider the problem of finding minimum-link rectilinear paths in
rectilinear polygonal domains in the plane. A path or a polygon is rectilinear
if all its edges are axis-parallel. Given a set $\mathcal{P}$ of $h$
pairwise-disjoint rectilinear polygonal obstacles with a total of $n$ vertices
in the plane, a minimum-link rectilinear path between two points is a
rectilinear path that avoids all obstacles with the minimum number of edges. In
this paper, we present a new algorithm for finding minimum-link rectilinear
paths among $\mathcal{P}$. After the plane is triangulated, with respect to any
source point $s$, our algorithm builds an $O(n)$-size data structure in
$O(n+h\log h)$ time, such that given any query point $t$, the number of edges
of a minimum-link rectilinear path from $s$ to $t$ can be computed in $O(\log
n)$ time and the actual path can be output in additional time linear in the
number of the edges of the path. The previously best algorithm computes such a
data structure in $O(n\log n)$ time.
