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On Some Polyhedra Covering Problems

Author

Listed:
  • Cao An Wang

    (Memorial University of Newfoundland)

  • Bo-Ting Yang

    (Memorial University of Newfoundland)

  • Binhai Zhu

    (Montana State University)

Abstract

Let P 0, P 1 be two simple polyhedra and let P 2 be a convex polyhedron in E 3. Polyhedron P 0 is said to be covered by polyhedra P 1 and P 2 if every point of P 0 is a point of P 1 ∪ P 2. The following polyhedron covering problem is studied: given the positions of P 0, P 1, and P 2 in the xy-coordinate system, determine whether or not P 0 can be covered by P 1 ∪ P 2 via translation and rotation of P 1 and P 2; furthermore, find the exact covering positions of these polyhedra if such a cover exists. It is shown in this paper that if only translation is allowed, then the covering problem of P 0, P 1 and P 2 can be solved in O(m 2 n 2(m + n)l)) polynomial time, where m, n, and l are the sizes of P 0, P 1, and P 2, respectively. The method can be easily extended to the problem in E d for any fixed d > 3.

Suggested Citation

  • Cao An Wang & Bo-Ting Yang & Binhai Zhu, 2000. "On Some Polyhedra Covering Problems," Journal of Combinatorial Optimization, Springer, vol. 4(4), pages 437-447, December.
    • Handle: RePEc:spr:jcomop:v:4:y:2000:i:4:d:10.1023_a:1009833410742
    DOI: 10.1023/A:1009833410742
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    Cited by:

    1. Olawale James, GBADEYAN, & Jamiu Ola, IDRIS & Kayode Olawale, KUMOYE, & Tayo Akindele, ZUBAIR,, 2016. "Assessing The Security Of Learning Spaces In Selected Primary Schools Within Ilorin Metropolis," Ilorin Journal of Business and Social Sciences, Faculty of Social Sciences, University of Ilorin, vol. 18(2), pages 179-198, October.

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