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Computing the relative neighborhood graph in the \(L_1\) and \(L_\infty\) metrics. (English) Zbl 0486.68063


MSC:

68R10 Graph theory (including graph drawing) in computer science
68Q25 Analysis of algorithms and problem complexity
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References:

[1] Toussaint, G. T., The relative neighborhood graph of a finite planar set, Pattern Recognition, 12, 261-268 (1980) · Zbl 0437.05050
[2] Toussaint, G. T., Pattern recognition and geometrical complexity, (Proc. 5th Int. Conf. on Pattern Recognition. Proc. 5th Int. Conf. on Pattern Recognition, Miami Beach, U.S.A. (1980)), 1324-1327
[3] Toussaint, G. T., Computational geometric problems in pattern recognition, (Technical Report No. SOCS-81.12 (1981), McGill University) · Zbl 0223.68020
[4] Lankford, P. M., Regionalization: theory and alternative algorithms, Geog. Anal., 5, 133-144 (1973)
[5] Bentley, J. L.; Maurer, H. A., Efficient worst-case data structures for range searching, Acta Informatica, 13, 155-168 (1980) · Zbl 0423.68029
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[8] Bentley, J. L., Multidimensional divide-and-conquer, Commun. Ass. Comput. Mach., 23, 214-229 (1980) · Zbl 0434.68049
[9] Coppersmith, D.; Lee, D. T.; Wong, C. K., An elementary proof of nonexistence of isometries between \(L_p^{k\) · Zbl 0424.68026
[10] Shamos, M. I.; Hoey, D., Closest point problems, (Proc. 16th Ann. Symp. on the Foundations of Computer Science. Proc. 16th Ann. Symp. on the Foundations of Computer Science, IEEE (1975)), 151-162
[11] Shamos, M. I., Computational geometry, (PhD Dissertation (1978), Yale University) · Zbl 0759.68037
[12] Lee, D. T.; Wong, C. K., Voronoi diagrams in \(L_1 (L_∞)\) metrics with 2-dimensional storage applications, SIAM J. Comput., 9, 200-211 (1980) · Zbl 0447.68111
[13] Lee, D. T., Two-dimensional Voronoi diagrams in the \(L_p\)-metric, J. Ass. Comput. Mach., 27, 604-618 (1980) · Zbl 0445.68053
[14] Supowit, K., The relative neighborhood graph with an application to minimum spanning trees, (Computer Science Technical Report (1980), University of Illinois) · Zbl 0625.68047
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