Abstract
In this paper, a new algorithm for constructing the relative neighborhood graph(RNG) of ann points set in Euclideank-dimensional space is presented, for fixedk≥3. The worst case running time of the algorithm isO(n 2−a(k)(logn)1−a(k)), fora(k)=2−(k+1), which is under the assumption that no three input points form an isosceles triangle. Previous algorithms needO(n 2) time. Our algorithm proceeds in two phases. First, a supergraph ofRNG withO(n) edges is constructed and then those edges which do not belong toRNG are eliminated.
Zusammenfassung
Wir stellen einen neuen Algorithmus vor, der fürn Punkte imk-dimensionalen euklidischen Raum für festesk≧3 den relativen Nachbarschafts-Graphen (RNG) liefert. Falls keine 3 Punkte ein gleichseitiges Dreieck bilden, verbessern wir die Laufzeit aufo(n 2) während bekannte AlgorithmenO(n 2) Zeit benötigen. Dabei scheint uns der Lösungsweg neu und interessant. Wir gehen in 2 Schritten vor. Zuerst konstruieren wir einen Graphen mitO(n) Kanten, welcher denRNG als Teilgraph enthält, und dann entfernen wir jene Kanten, die nicht zumRNG gehören.
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This research was partially supported by the National Science Council of Republic of China under the grant NSC 79-0408-E009-16.
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Su, TH., Chang, RC. On constructing the relative neighborhood graphs in EuclideanK-dimensional spaces. Computing 46, 121–130 (1991). https://doi.org/10.1007/BF02239166
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DOI: https://doi.org/10.1007/BF02239166