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

02/14/2023

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by   Kerem Geva, et al.

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Let E={e_1,…,e_n} be a set of C-oriented disjoint segments in the plane, where C is a given finite set of orientations that spans the plane, and let s and t be two points. in C, its opposite orientation is also in C.) We seek a minimum-link C-oriented tour of E, that is, a polygonal path π from s to t that visits the segments of E in order, such that, the orientations of its edges are in C and their number is minimum. We present an algorithm for computing such a tour in O(|C|^2 · n^2) time. This problem already captures most of the difficulties occurring in the study of the more general problem, in which E is a set of not-necessarily-disjoint C-oriented polygons.