Touring a sequence of disjoint polygons: Complexity and extension

Ahadi, Arash; Mozafari, Amirhossein; Zarei, Alireza

doi:10.1016/j.tcs.2014.06.019

Cited by 16 publications

(14 citation statements)

References 6 publications

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“…Dror et al asked as an open problem whether the TPP is NP-hard when the polygons are non-convex and pairwise disjoint. This was positively answered by Ahadi et al [16], even when each polygon consists of at most two line-segments. Ahadi et al also give an approximation algorithm for the Touring Object Problem which deals with finding the shortest route to visit a set of solid polygons that the tour cannot pass through.…”

Section: Touring Polygons Problemmentioning

confidence: 93%

A review of cutting path algorithms for laser cutters

Dewil

Vansteenwegen

Cattrysse

2016

Int J Adv Manuf Technol

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This paper presents a review of the literature on generating cutting paths for laser cutting machines. Firstly, the cutting path problem is defined including all relevant technical side constraints which exist plentifully in laser cutting. Secondly, a former classification method is updated to include all types of cutting path problems. Thirdly, a comprehensive review of solution methods and related applications is presented. Throughout the literature review, trends in research in cutting path generation and interesting areas for future research are identified.

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Section: Touring Polygons Problemmentioning

confidence: 93%

A review of cutting path algorithms for laser cutters

Dewil

Vansteenwegen

Cattrysse

2016

Int J Adv Manuf Technol

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“…TPP is a generalization of the traveling salesman problem (TSP) which is NP-hard if the order of the polygons is not given [2,4,5]. We focus on solving the problem where the polygons must be visited in order.…”

Section: Current Workmentioning

confidence: 99%

2-Approximate Algorithm for Touring a Sequence of Pairwise Disjoint Simple Polygons

Shun¹,

Jiang²

2017

dtcse

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Abstract. In this paper, a 2-approximate algorithm is described to answer the previously open problem "What is the complexity of the TPP for disjoint non-convex simple polygons" which is known to NP-hard. We provide a O(kn) approximate algorithm, where k is polygon counts, and n is the number of vertexes of the polygons, to efficiently find a path which is 2 times at most than the shortest path. To solve this problem, we transform all of simple polygons into corresponding convex polygons, then process the shortest path of convex polygons according to the parity of polygons sequence and finally obtain the approximate path of simple polygons.

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“…The goal is to find the shortest path that starts from s, visits all convex polygons according to their order and ends at t [3]. In Fig.…”

Section: Introductionmentioning

confidence: 99%

“…(3). What all these problems have in common is that the shortest visiting path in the given order needed to be found [3]. If the visited order is not specified, it becomes the classical Traveling Salesperson Problem with neighborhoods, which is NP-hard [10].…”

Section: Introductionmentioning

confidence: 99%

“…They also proved the TPP is NP-hard for the case that they are intersected and non-convex polygons [4,11]. Arash Ahadi et al also proved that TPP is NP-hard when the polygons are pairwise disjoint [3]. Several approximation algorithms have been proposed for the case of disjoint convex polygons, for example, Fajie Li and Reinhard Kettle in 2007 gave an approximate algorithm in K( ε )·O(n) time by applying the rubber-band algorithm for sequences of convex polygons, where…”

Section: Introductionmentioning

confidence: 99%

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A New Algorithm for the Shortest Path of Touring Disjoint Convex Polygons

Wang¹,

Jiang²,

Deng³

et al. 2015

TOAUTOCJ

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Given a start point s, a target point t, and a sequence of k disjoint convex polygons in the plane, finding the shortest path from s to t which visits each convex polygon in the given order is our focus. In this paper, we present an improved method to compute the shortest path based on the last step path maps by Dror et al. Instead of using of point location in previous algorithm, we propose an efficient method of locating the points in the path with linear query and make the data structures much simpler. Our improved algorithm gives the O(nk) running time which improves upon the time O(nklog(n/k)) by Dror etal., where n is the total number of vertices of all polygons. Furthermore, we have implemented this algorithm by programming. The result shows that our algorithm is correct and efficient..

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Touring a sequence of disjoint polygons: Complexity and extension

Cited by 16 publications

References 6 publications

A review of cutting path algorithms for laser cutters

A review of cutting path algorithms for laser cutters

2-Approximate Algorithm for Touring a Sequence of Pairwise Disjoint Simple Polygons

A New Algorithm for the Shortest Path of Touring Disjoint Convex Polygons

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