Traversing the Machining Graph

  • Danny Z. Chen
  • Rudolf Fleischer
  • Jian Li
  • Haitao Wang
  • Hong Zhu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4168)


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 ε>0 is any constant.


Planar Graph Tool Path Dual Graph Outerplanar Graph Bounded Degree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Danny Z. Chen
    • 1
  • Rudolf Fleischer
    • 2
  • Jian Li
    • 2
  • Haitao Wang
    • 2
  • Hong Zhu
    • 2
  1. 1.Department of Computer Science and EngineeringUniversity of Notre DameNotre DameUSA
  2. 2.Department of Computer Science and Engineering, Shanghai Key Laboratory of Intelligent Information ProcessingFudan UniversityShanghaiChina

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