BibTex Citation Data :
@article{JFMA12053, author = {Marco Ripà}, title = {GENERAL UNCROSSING COVERING PATHS INSIDE THE AXIS-ALIGNED BOUNDING BOX}, journal = {Journal of Fundamental Mathematics and Applications (JFMA)}, volume = {4}, number = {2}, year = {2021}, keywords = {Optimization; Link distance; Minimum bounding box; Covering path; MΛI-algorithm}, abstract = { Given the finite set of n _1 ⋅ n _2 ⋅ ... ⋅ n _ k points G ( n _1, n _2,..., n _ k ) in R ^𝑘 such that n _ k ≥ ...≥ n _2 ≥ n _ 1∈ Z +, we introduce a new algorithm, called M Λ I, which returns an uncrossing covering path inside the minimum axis-aligned bounding box [0, n _1−1]×[0, n _2−1]×...×[0, n _ k −1], consisting of 3 ⋅ ( n _1 ⋅ n _2 ⋅ ... ⋅ n _ k −1)−2 links of prescribed length n _ k −1 units. Thus, for any n _ k ≥3, the link length of the covering path provided by our M Λ I-algorithm is smaller than the cardinality of the set G ( n _1, n _2,..., n _ k ). Furthermore, assuming k >2, we present an uncrossing covering path for G ( 3 , 3 ,..., 3 ), comprising only 20*3^( k −3)−2 two units long edges, which is constrained by the axis-aligned bounding box [0,4− √3 ]×[0,4− √3 ]×[0, 2 ]×...×[0, 2 ]. }, issn = {2621-6035}, pages = {154--166} doi = {10.14710/jfma.v4i2.12053}, url = {https://ejournal2.undip.ac.id/index.php/jfma/article/view/12053} }
Refworks Citation Data :
Given the finite set of n_1⋅n_2⋅...⋅n_k points G(n_1,n_2,...,n_k) in R^𝑘 such that n_k≥...≥n_2≥n_1∈Z+, we introduce a new algorithm, called MΛI, which returns an uncrossing covering path inside the minimum axis-aligned bounding box [0,n_1−1]×[0,n_2−1]×...×[0,n_k−1], consisting of 3⋅(n_1⋅n_2⋅...⋅n_k−1)−2 links of prescribed length n_k−1 units. Thus, for any n_k≥3, the link length of the covering path provided by our MΛI-algorithm is smaller than the cardinality of the set G(n_1,n_2,...,n_k). Furthermore, assuming k>2, we present an uncrossing covering path for G(3,3,...,3), comprising only 20*3^(k−3)−2 two units long edges, which is constrained by the axis-aligned bounding box [0,4−√3]×[0,4−√3]×[0,2]×...×[0,2].
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