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

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Abstract

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.

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Authors and Affiliations

  1. Department of Computer Science and Technology, Tsinghua National Lab for Information Science and Technology, Tsinghua University, Beijing, P.R. China

    Yong-Jin Liu & Wen-Qi Zhang

  2. Department of Mechanical Engineering, Hong Kong University of Science and Technology, Kowloon, Hong Kong

    Kai Tang

Authors
  1. Yong-Jin Liu
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  2. Wen-Qi Zhang
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  3. Kai Tang
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Correspondence to Yong-Jin Liu.

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Liu, YJ., Zhang, WQ. & Tang, K. Some notes on maximal arc intersection of spherical polygons: its  \(\mathcal{NP}\) -hardness and approximation algorithms. Vis Comput 26, 287–292 (2010). https://doi.org/10.1007/s00371-009-0406-5

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  • DOI: https://doi.org/10.1007/s00371-009-0406-5

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