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Touring convex polygons in polygonal domain fences

Ahadi, A ; Sharif University of Technology | 2017

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  1. Type of Document: Article
  2. DOI: 10.1007/978-3-319-71147-8_5
  3. Publisher: Springer Verlag , 2017
  4. Abstract:
  5. In the touring polygons problem (TPP), for a given sequence (s= P0, P1, ⋯, Pk, t = Pk+1) of polygons in the plane, where s and t are two points, the goal is to find a shortest path that starts from s, visits each of the polygons in order and ends at t. In the constrained version of TPP, there is another sequence (F0, ⋯, Fk) of polygons called fences, and the portion of the path from Pi to Pi+1 must lie inside the fence Fi. TPP is NP-hard for disjoint non-convex polygons, while TPP and constrained TPP are polynomially solvable when the polygons are convex and the fences are simple polygons. In this work, we present the first polynomial time algorithm for solving constrained TPP when the fences are polygonal domains (polygons with holes). Since, the safari problem is a special case of TPP, our algorithm can be used for solving safari problem inside polygons with holes. © Springer International Publishing AG 2017
  6. Keywords:
  7. Combinatorial optimization ; Fences ; Optimization ; Polynomial approximation ; Problem solving ; Convex polygon ; Nonconvex polygons ; Polygonal domain ; Polygons with holes ; Polynomial-time algorithms ; Polynomially solvable ; Shortest path ; Simple polygon ; Geometry
  8. Source: 11th International Conference on Combinatorial Optimization and Applications, COCOA 2017, 16 December 2017 through 18 December 2017 ; Volume 10628 LNCS , 2017 , Pages 61-75 ; 03029743 (ISSN); 9783319711461 (ISBN)
  9. URL: https://link.springer.com/chapter/10.1007/978-3-319-71147-8_5