The relative neighbourhood graph of a finite planar set. (English) Zbl 0437.05050


05C99 Graph theory
05C05 Trees
05C75 Structural characterization of families of graphs
Full Text: DOI


[1] Zahn, C. T., Graph-theoretical methods for detecting and describing gestalt clusters, IEEE Trans. Comput. C-20, 68-86 (1971) · Zbl 0264.68040
[2] Rosenberg, B.; Langridge, D. J., A computational view of perception, Perception, 2, 415-424 (1973)
[3] Lewis, B. A.; Robinson, J. S., Triangulation of planar regions with applications, Comput. J., 21, 324-332 (1978) · Zbl 0386.68090
[4] Sibson, R., Locally equiangular triangulations, Comput. J., 21, 243-245 (1978)
[5] Green, P. J.; Sibson, R., Computing Dirichlet tessellations in the plane, Comput. J., 21, 168-173 (1978) · Zbl 0377.52001
[6] Rhynsburger, D., Analytic delineation of Thiessen polygons, Geogrl Anal., 5, 133-144 (1973)
[7] 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
[8] Lankford, P. M., Regionalization: theory and alternative algorithms, Geogrl Anal., 1, 196-212 (1969)
[9] Arnheim, R., Art and Visual Perception, ((1974), University of California Press), 54
[10] Bentley, J. L.; Shamos, M., Divide and conquer for linear expected time, Inf. Process. Lett., 7, 87-91 (1978) · Zbl 0404.68046
[11] Toussaint, G. T.; Akl, S. G.; Devroye, L. P., Efficient convex hull algorithms for points in two and more dimensions, (Technical Report. No. SOCS 78.5 (1978), McGill University)
[12] Devroye, L., A note on finding convex hulls via maximal vectors (1979), McGill University, manuscript
[13] Gilbert, E. N., Random minimal trees, SIAM J. appl. Math., 13, 376-387 (1965) · Zbl 0156.19102
[14] Roberts, F. D.K., Random minimal trees, Biometrika, 55, 255-258 (1968) · Zbl 0153.47506
[15] O’Callaghan, J. F., An alternative definition for neighbourhood of a point, IEEE Trans. Comput. C-24, 1121-1125 (1975) · Zbl 0313.68076
[16] Jarvis, R. A., Shared near neighbour maximal spanning trees for cluster analysis, (Proc. 4th Int. Joint Conf. on Pattern Recognition (1978)), 308-313, Kyoto, Japan
[17] Harary, F., Graph Theory (1972), Addison Wesley: Addison Wesley Reading, MA · Zbl 0797.05064
[18] Weide, B. W., Statistical methods in algorithm design and analysis, (Ph.D. thesis (August 1978), Department of Computer Science, Carnegie-Mellon University)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.