Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-23T22:37:44.096Z Has data issue: false hasContentIssue false

Determining shortest networks in the Euclidean plane

Published online by Cambridge University Press:  17 April 2009

J.F. Weng
Affiliation:
Department of MathematicsThe University of MelbourneParkville Vic 3052, Australia
Rights & Permissions [Opens in a new window]

Abstract

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Abstracts of Australasian Ph.D. Theses
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Cockayne, E.J., ‘On the efficiency of the algorithm for Steiner minimal trees’, SIAM J. Appl. Math. 18 (1970), 150159.Google Scholar
[2]Du, D.Z., Hwang, F.K. and Weng, J.F., ‘Steiner minimal trees on zigzag lines’, Trans. Amer. Math. Soc. 278 (1983), 149156.Google Scholar
[3]Du, D.Z., Hwang, F.K. and Weng, J.F., ‘Steiner minimal trees on regular polygons’, Discrete Comput. Geom. 2 (1987), 6587.Google Scholar
[4]Garey, M.R., Graham, R.L. and Johnson, D.S., ‘The complexity of computing Steiner minimal trees’, SIAM J. Appl. Math. 32 (1977), 835859.Google Scholar
[5]Gilbert, E.N. and Pollack, H.O., ‘Steiner minimal trees’, SIAM J. Appl. Math. 16 (1986), 129.Google Scholar
[6]Kuhn, H.W., ‘Steiner's problem revised’, in Studies in optimization, (G.B. Dantzig and B.C. Eavas, Editors), Studies in Math. 10 (Math. Assoc. Amer., 1975), pp. 5370.Google Scholar
[7]Pollak, H.O., ‘Some remarks on the Steiner problem’, J. Combin. Theory Ser. A 24 (1978), 278295.CrossRefGoogle Scholar
[8]Rubinstein, J.H. and Thomas, D.A., ‘A variational approach to the Steiner network problem’, Annals Oper. Res. 33 (1991), 481499.Google Scholar