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Let $E=\{e_1,\ldots,e_n\}$ be a set of $C$-oriented disjoint segments in theplane, where $C$ is a given finite set of orientations that spans the plane,and let $s$ and $t$ be two points. %(We also require that for each orientationin $C$, its opposite orientation is also in $C$.) We seek a minimum-link$C$-oriented tour of $E$, that is, a polygonal path $\pi$ from $s$ to $t$ thatvisits the segments of $E$ in order, such that, the orientations of its edgesare in $C$ and their number is minimum. We present an algorithm for computingsuch a tour in $O(|C|^2 \cdot n^2)$ time. This problem already captures most ofthe difficulties occurring in the study of the more general problem, in which$E$ is a set of not-necessarily-disjoint $C$-oriented polygons.

Minimum-link $C$-Oriented Paths Visiting a Sequence of Regions in the Plane