The Visual Computer

, Volume 26, Issue 4, pp 287–292 | Cite as

Some notes on maximal arc intersection of spherical polygons: its  \(\mathcal{NP}\) -hardness and approximation algorithms

  • Yong-Jin LiuEmail author
  • Wen-Qi Zhang
  • Kai Tang
Original Article


Finding a sequence of workpiece orientations such that the number of setups is minimized is an important optimization problem in manufacturing industry. In this paper we present some interesting notes on this optimal workpiece setup problem. These notes show that (1) The greedy algorithm proposed in Comput. Aided Des. 35 (2003), pp. 1269–1285 for the optimal workpiece setup problem has the performance ratio bounded by O(ln n−ln ln n+0.78), where n is the number of spherical polygons in the ground set; (2) In addition to greedy heuristic, linear programming can also be used as a near-optimal approximation solution; (3) The performance ratio by linear programming is shown to be tighter than that of greedy heuristic in some cases.

Spherical polygons intersection NC machining \(\mathcal{NP}\) -hard problem Approximation algorithms 


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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of Computer Science and Technology, Tsinghua National Lab for Information Science and TechnologyTsinghua UniversityBeijingP.R. China
  2. 2.Department of Mechanical EngineeringHong Kong University of Science and TechnologyKowloonHong Kong

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