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Traversing the Machining Graph

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Algorithms – ESA 2006 (ESA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4168))

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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 ε>0 is any constant.

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN, 46556, USA

    Danny Z. Chen

  2. Department of Computer Science and Engineering, Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai, China

    Rudolf Fleischer, Jian Li, Haitao Wang & Hong Zhu

Authors
  1. Danny Z. Chen
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  2. Rudolf Fleischer
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  3. Jian Li
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  4. Haitao Wang
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  5. Hong Zhu
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Editor information

Editors and Affiliations

  1. Microsoft Research, One Microsoft Way, Redmond, WA 98052, USA and School of Computer Science, Tel-Aviv University, 69978, Tel-Aviv, Israel

    Yossi Azar

  2. Department of Computer Science, University of Leicester, University Road, LE1 7RH, Leicester, UK

    Thomas Erlebach

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© 2006 Springer-Verlag Berlin Heidelberg

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Chen, D.Z., Fleischer, R., Li, J., Wang, H., Zhu, H. (2006). Traversing the Machining Graph. In: Azar, Y., Erlebach, T. (eds) Algorithms – ESA 2006. ESA 2006. Lecture Notes in Computer Science, vol 4168. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11841036_22

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  • DOI: https://doi.org/10.1007/11841036_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-38875-3

  • Online ISBN: 978-3-540-38876-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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