Traversing the machining graph

Authors:
Danny Z. Chen;Rudolf Fleischer;Jian Li;Haitao Wang;Hong Zhu
Affiliations:
Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN;Department of Computer Science and Engineering, Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai, China;Department of Computer Science and Engineering, Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai, China;Department of Computer Science and Engineering, Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai, China;Department of Computer Science and Engineering, Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai, China
Venue:
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Year:
2006

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Abstract

Zigzag pocket machining (or 2D-milling) plays an important role in the manufacturing industry. The objective is to minimize the number of tool retractions in the zigzag machining path for a given pocket (i.e., a planar domain). We give an optimal linear time dynamic programming algorithm for simply connected pockets, and a linear plus O(1)O(h) time optimal algorithm for pockets with h holes. If the dual graph of the zigzag line segment partition of the given pocket is a partial k-tree of bounded degree or a k- outerplanar graph, for a fixed k, we solve the problem optimally in time O(n logn). Finally, we propose a polynomial time algorithm for finding a machining path for a general pocket with h holes using at most OPT+εh retractions, where OPT is the smallest possible number of retractions and ε0 is any constant.