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Touring disjoint polygons problem is NP-hard

Ahadi, A ; Sharif University of Technology | 2013

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  1. Type of Document: Article
  2. DOI: 10.1007/978-3-319-03780-6_31
  3. Publisher: 2013
  4. Abstract:
  5. In the Touring Polygons Problem (TPP) there is a start point s, a sequence of simple polygons P = (P1,...,Pk) and a target point t in the plane. The goal is to obtain a path of minimum possible length that starts from s, visits in order each of the polygons in P and ends at t. This problem has a polynomial time algorithm when the polygons in P are convex and is NP-hard in general case. But, it has been open whether the problem is NP-hard when the polygons are pairwise disjoint. In this paper, we prove that TPP is also NP-hard when the polygons are pairwise disjoint in any Lp norm even if each polygon consists of at most two line segments. This result solves an open problem from STOC '03 and complements recent approximation results
  6. Keywords:
  7. Approximation results ; NP-hard ; Polynomial-time algorithms ; Start point ; Target point ; Two-line ; Simple polygon ; Algorithms ; Combinatorial optimization ; Polynomial approximation ; Geometry ; Optimization
  8. Source: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) Volume 8287 LNCS, 2013, Pages 351-360 ; Volume 8287 , 2013 , Pages 351-360 ; 03029743 (ISSN) ; 9783319037790 (ISBN)
  9. URL: http://link.springer.com/chapter/10.1007%2F978-3-319-03780-6_31