Abstract
The rectilinear Steiner minimum tree for a set of points is the shortest network interconnecting points in the set with rectilinear distance. Computing the rectilinear Steiner minimum tree is NP-hard [2]. In this paper, we present two polynomial-time computable special cases. As an application, we also give a simple way to compute the rectilinear Steiner minimum tree for four, five, and six points.
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Support in part by the grant MIP-9123945
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References
M.R. Garey and D.S. Johnson, “The rectilinear Steiner tree problem is NP-complete,” SIAM Journal of Applied Mathematics, 32 (1977) 826–834
M. Hanan, “On Steiner’s problem with rectilinear distance,” SIAM J. Appl. Math., 16 (1966) 255–265
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© 1997 Springer-Verlag Berlin Heidelberg
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Du, DZ., Shragowitz, E., Wan, PJ. (1997). Two Special Cases for Rectilinear Steiner Minimum Trees. In: Pardalos, P.M., Hearn, D.W., Hager, W.W. (eds) Network Optimization. Lecture Notes in Economics and Mathematical Systems, vol 450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59179-2_11
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DOI: https://doi.org/10.1007/978-3-642-59179-2_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-62541-4
Online ISBN: 978-3-642-59179-2
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