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Touring Polygons: An Approximation Algorithm

  • Amirhossein Mozafari
  • Alireza Zarei
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7643)

Abstract

In this paper, we introduce a new version of the shortest path problem appeared in many applications. In this problem, there is a start point s, an end point t, an ordered sequence \(\cal{S}\)=(S 0 = s,S 1,...,S k ,S k + 1 = t) of sets of polygons, and an ordered sequence \(\cal{F}\)=(F 0,...,F k ) of simple polygons named fences in \(\Re^2\) such that each fence F i contains polygons of S i and S i + 1. The goal is to find a path of minimum possible length from s to t which orderly touches the sets of polygons of \(\cal{S}\) in at least one point supporting the fences constraints. This is the general version of the previously answered Touring Polygons Problem (TPP). We prove that this problem is NP-Hard and propose a precision sensitive FPTAS algorithm of O(k 2 n 2/ε 2) time complexity where n is the total complexity of polygons and fences.

Keywords

Computational geometry approximation algorithm touring polygons minimum link path 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Amirhossein Mozafari
    • 1
  • Alireza Zarei
    • 1
  1. 1.Department of Mathematical SciencesSharif University of TechnologyIran

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