Minimal link visibility paths inside a simple polygon

Alsuwaiyel, M H; Lee, D. T.

doi:10.1016/0925-7721(93)90027-4

Cited by 23 publications

(15 citation statements)

References 10 publications

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“…Most relevant to our problem is the prior work on minimumlink watchman tours: see [2,3,8] for hardness and approximation results, and [14,36] for combinatorial bounds. However, in these problems the watchman is assumed to see arbitrarily far, making them distinct from our tour cover problems.…”

Section: Approximation Factors Achieved By Our (Polynomial-time) Algomentioning

confidence: 99%

Optimal Covering Tours with Turn Costs

Arkin¹,

Bender²,

Demaine³

et al. 2005

SIAM J. Comput.

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Abstract. We give the first algorithmic study of a class of "covering tour" problems related to the geometric Traveling Salesman Problem: Find a polygonal tour for a cutter so that it sweeps out a specified region ("pocket"), in order to minimize a cost that depends mainly on the number of turns. These problems arise naturally in manufacturing applications of computational geometry to automatic tool path generation and automatic inspection systems, as well as arc routing ("postman") problems with turn penalties. We prove the NP-completeness of minimum-turn milling and give efficient approximation algorithms for several natural versions of the problem, including a polynomialtime approximation scheme based on a novel adaptation of the m-guillotine method.

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Section: Approximation Factors Achieved By Our (Polynomial-time) Algomentioning

confidence: 99%

Optimal Covering Tours with Turn Costs

Arkin¹,

Bender²,

Demaine³

et al. 2005

SIAM J. Comput.

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“…Alsuwaiyel and Lee [1,2] show that if P is a simple polygon, then the minimum-link watchman route problem is NP-complete, and they give a constant-factor approximation algorithm. Their approximation algorithm does not at all apply to the case of holes (obstacles).…”

Section: Introductionmentioning

confidence: 99%

Minimum-link watchman tours

Arkin

Mitchell

Piatko

2003

Information Processing Letters

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We consider the problem of computing a watchman route in a polygon with holes. We show that the problem of finding a minimum-link watchman route is NP-complete, even if the holes are all convex. The proof is based on showing that the related problem of finding a minimum-link tour on a set of points in the plane is NP-complete. We provide a provably good approximation algorithm that achieves an approximation factor of O(log n).

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“…Alsuwaiyel and Lee [10] showed that nding a Hamiltonian (s; X; t)-path (not necessarily simple) in a simple polygon P is NP-complete. Their proof works even in the special case when X is restricted to be the vertex set of P .…”

Section: Related Workmentioning

confidence: 99%

Time complexity of two disjoint simple paths

Razzazi

Sepahvand

2017

Scientia Iranica

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Abstract. Finding two disjoint simple paths on two given sets of points is a geometric problem introduced by Je Erickson. This problem has various applications in computational geometry, e.g. robot motion planning, generating polygon, etc. We will present a reduction from planar Hamiltonian path to this problem, and prove that it is NPcomplete. To the best of our knowledge, no study has considered its complexity up until now. We also present a reduction from planar Hamiltonian path problem to the problem of \ nding a path on given points in the presence of arbitrary obstacles" and prove that it is also NP-complete. Also, we present a heuristic algorithm with time complexity of O(n 4 ) to solve this problem. The proposed algorithm rst calculates the convex hull for each of the entry points and then produces two simple paths on the two entry point sets.

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Minimal link visibility paths inside a simple polygon

Cited by 23 publications

References 10 publications

Optimal Covering Tours with Turn Costs

Optimal Covering Tours with Turn Costs

Minimum-link watchman tours

Time complexity of two disjoint simple paths

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