Combinatorial Complexity of Translating a Box in Polyhedral 3-Space

  title={Combinatorial Complexity of Translating a Box in Polyhedral 3-Space},
  author={Dan Halperin and Chee-Keng Yap},
  booktitle={Symposium on Computational Geometry},
We study the space of free translations of a box amidst polyhedral obstacles with <italic>n</italic> features. We show that the combinatorial complexity of this space is <italic>O(n<supscrpt>2</supscrpt>α(n))</italic> where <italic>α(n)</italic> is the inverse Ackermann function. Our bound is within an <italic>α(n)</italic> factor off the lower bound, and it constitutes an improvement of almost an order of magnitude over the best previously known (and naive) bound for this problem, <italic>O(n… CONTINUE READING

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