IWOCA 2012: Combinatorial Algorithms pp 110-121

# 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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