Determining an Optimal Penetration Among Weighted Regions in Two and Three Dimensions
Identifieur interne : 009360 ( Main/Exploration ); précédent : 009359; suivant : 009361Determining an Optimal Penetration Among Weighted Regions in Two and Three Dimensions
Auteurs : Danny Z. Chen [États-Unis] ; Ovidiu Daescu [États-Unis] ; Xiaobo Sharon Hu [États-Unis] ; Xiaodong Wu [États-Unis] ; Jinhui Xu [États-Unis]Source :
- Journal of Combinatorial Optimization [ 1382-6905 ] ; 2001-03-01.
English descriptors
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.
Url:
DOI: 10.1023/A:1009885517653
Affiliations:
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