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Computational Complexity of Robot Arm Simulation Problems

  • Tianfeng FengEmail author
  • Takashi Horiyama
  • Yoshio Okamoto
  • Yota Otachi
  • Toshiki Saitoh
  • Takeaki Uno
  • Ryuhei Uehara
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10979)

Abstract

We consider a simulation problem of a general mechanism by a robot arm. A robot arm can be modeled by a path P, and the target is modeled by a general graph G. Then the problem asks if there is an edge-weighted Eulerian path of G spanned by P. We first show that it is strongly NP-hard even if edge lengths are restricted. Then we consider two different variants of this problem. We first allow the edges in P to be elastic, and minimize the elastic ratio when G is a path. Second, we allow P to cover an edge of G twice or more. The problem is weakly NP-hard even if G is an edge. We thus assume that each edge of G is covered by P exactly twice, and obtain three hardness results and one polynomial-time algorithm when G and edge lengths are restricted.

Keywords

Edge-weighted Eulerian path problem Graph spanning problem Linkage Robot arm 

References

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    Demaine, E.D., O’Rourke, J.: Geometric Folding Algorithms. Cambridge University Press, Cambridge (2007)Google Scholar
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    Kupferman, O., Vardi, G.: Eulerian paths with regular constraints. In: 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), vol. 58, 62:1–62:15 (2016)Google Scholar
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    Michael, R.G., David, S.J.: Computers and Intractability: A Guide to the Theory of NP-Completeness, pp. 90–91. W. H. Freeman Co., San Francisco (1979)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Tianfeng Feng
    • 1
    Email author
  • Takashi Horiyama
    • 2
  • Yoshio Okamoto
    • 3
  • Yota Otachi
    • 4
  • Toshiki Saitoh
    • 5
  • Takeaki Uno
    • 6
  • Ryuhei Uehara
    • 1
  1. 1.Japan Advanced Institute of Science and Technology (JAIST)NomiJapan
  2. 2.Saitama UniversitySaitamaJapan
  3. 3.RIKEN Center for Advanced Intelligence ProjectUniversity of Electro-CommunicationsChofuJapan
  4. 4.Kumamoto UniversityKumamotoJapan
  5. 5.Kyushu Institute of TechnologyKitakyushuJapan
  6. 6.National Institute of InformaticsTokyoJapan

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