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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
In this paper, for a function f() and a predicate p(), their corresponding tables (or arrays in program) are denoted by f[] and p[], respectively.
References
Demaine, E.D., O’Rourke, J.: Geometric Folding Algorithms. Cambridge University Press, Cambridge (2007)
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)
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)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Feng, T. et al. (2018). Computational Complexity of Robot Arm Simulation Problems. In: Iliopoulos, C., Leong, H., Sung, WK. (eds) Combinatorial Algorithms. IWOCA 2018. Lecture Notes in Computer Science(), vol 10979. Springer, Cham. https://doi.org/10.1007/978-3-319-94667-2_15
Download citation
DOI: https://doi.org/10.1007/978-3-319-94667-2_15
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-94666-5
Online ISBN: 978-3-319-94667-2
eBook Packages: Computer ScienceComputer Science (R0)