Title :
On the performance of maximal intersection of spherical polygons by arcs
Author :
Liu, Yong-Jin ; Zhang, Wen-Qi ; Tang, Kai
Author_Institution :
Dept. of Comput. Sci. & Technol., Tsinghua Univ., Beijing, China
Abstract :
An important real-world optimization problem in manufacturing industry is to determine optimal workpiece setups for 4-axis NC machining. In this paper we reveal some interesting relations between this optimal workpiece setup problem and the two classic NP-hard problems in complexity theory (i.e, the vertex cover problem and the set cover problem). These relations immediately show the following results. First the optimal workpiece setup problem is NP-hard. Secondly, 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.
Keywords :
computational complexity; machining; numerical control; optimisation; 4-axis NC machining; NP-hard problems; arcs; maximal intersection; real-world optimization problem; spherical polygons; CADCAM; Complexity theory; Computer aided manufacturing; Computer science; Gaussian processes; Greedy algorithms; Machining; Manufacturing industries; Mechanical engineering; Solid modeling;
Conference_Titel :
Computer-Aided Design and Computer Graphics, 2009. CAD/Graphics '09. 11th IEEE International Conference on
Conference_Location :
Huangshan
Print_ISBN :
978-1-4244-3699-6
Electronic_ISBN :
978-1-4244-3701-6
DOI :
10.1109/CADCG.2009.5246868
