2017
DOI: 10.24200/sci.2017.4116
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Time complexity of two disjoint simple paths

Abstract: 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 \ … Show more

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Cited by 5 publications
(3 citation statements)
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“…Kaneko [6] generalized this theorem to general graphs. For other results on graph factors, see [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21].…”
Section: Introductionmentioning
confidence: 99%
“…Kaneko [6] generalized this theorem to general graphs. For other results on graph factors, see [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21].…”
Section: Introductionmentioning
confidence: 99%
“…Deepak et al tried to add some modifications to stand‐alone artificial intelligent techniques for performance improvement and compared the results of hybridisation with stand‐alone methods. Razzazi et al proposed an idea regarding time complexity of two disjoint simple paths. Their study is primarily applicable to path planning of mobile robots.…”
Section: Introductionmentioning
confidence: 99%
“…Singh et al [17][18][19] discussed the use of computational intelligence for smooth and collisionfree path generation for wheeled mobile robots. Razzazi and Sepahvand [20] proposed an idea regarding time complexity of two disjoint simple paths. Their study is primarily applicable to path planning of mobile robots.…”
Section: Introductionmentioning
confidence: 99%