Determining an Optimal Penetration Among Weighted Regions in Two and Three Dimensions

Danny Z. Chen (), Ovidiu Daescu (), Xiaobo (Sharon) Hu (), Xiaodong Wu () and Jinhui Xu ()
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Danny Z. Chen: University of Notre Dame
Ovidiu Daescu: University of Notre Dame
Xiaobo (Sharon) Hu: University of Notre Dame
Xiaodong Wu: University of Notre Dame
Jinhui Xu: University of Notre Dame

Journal of Combinatorial Optimization, 2001, vol. 5, issue 1, No 5, 59-79

Abstract: Abstract We present efficient algorithms for solving the problem of computing an optimal penetration (a ray or a semi-ray) among weighted regions in 2-D and 3-D spaces. This problem finds applications in several areas, such as radiation therapy, geological exploration, and environmental engineering. Our algorithms are based on a combination of geometric techniques and optimization methods. Our geometric analysis shows that the d-D (d = 2, 3) optimal penetration problem can be reduced to solving O(n 2(d−1)) instances of certain special types of non-linear optimization problems, where n is the total number of vertices of the regions. We also give implementation results of our 2-D algorithms.

Keywords: optimal penetration; geometric techniques; optimization; weighted region (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (2)

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DOI: 10.1023/A:1009885517653

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