On some distance problems in fixed orientations
SIAM Journal on Computing
Reducing the Steiner problem in a normal space
SIAM Journal on Computing
The Steiner tree problem in orientation metrics
Journal of Computer and System Sciences
The Steiner Minimal Tree Problem in the lambda-Geormetry Plane
ISAAC '96 Proceedings of the 7th International Symposium on Algorithms and Computation
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In this paper, we study the Steiner tree problem in the λ4- geometry plane in which any line, half line or line segment must go in an orientation of iπ/4 with the positive x-axis, 0 ≤ i ≤ 7, and the distance between two points is the length of the shortest polygonal path connecting them. We show that for any set of n terminal points, there exists a Steiner minimal tree interconnecting these terminal points such that all Steiner points are in G⌈2n/3⌉-1, the (⌈2n/3⌉ - 1)st-generation grid points formed by the n terminal points. Our result improves previous known result which guarantees that for any set of n terminal points, there is a Steiner minimal tree in which all Steiner points are in Gn-2.