Touring a Sequence of Line Segments in Polygonal Domain Fences

In this paper, we consider the problem of touring a sequence of line segments in presence of polygonal domain fences. In this problem there is a sequence S = (s = S0, . . . , Sk, Sk+1 = t) in which s and t are respectively start and target points and S1, . . . , Sk are line segments in the plane. Also, we are given a sequence F = (F0, . . . , Fk) of planar polygonal domains called fences such that Si ∪ Si+1 ⊂ Fi. The goal is to obtain a shortest path from s to t which visits in order each of the segments in S in such a way that the portion of the path from Si to Si+1 lies in Fi. In 2003, Dror et. al. proposed a polynomial time algorithm for this problem when the fences are simple polygons. Here, we propose an efficient polynomial time algorithm for this problem when the fences are polygonal domains (simple polygons with some polygonal holes inside).