TY - GEN

T1 - The steiner tree problem in λ4-geometry plane

AU - Lin, Guo Hui

AU - Xue, Guoliang

PY - 1998

Y1 - 1998

N2 - 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⌋r - 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.

AB - 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⌋r - 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.

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U2 - 10.1007/3-540-49381-6_35

DO - 10.1007/3-540-49381-6_35

M3 - Conference contribution

AN - SCOPUS:84867462258

SN - 3540653856

SN - 9783540653851

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 327

EP - 337

BT - Algorithms and Computation - 9th International Symposium, ISAAC'98, Proceedings

PB - Springer Verlag

T2 - 9th Annual International Symposium on Algorithms and Computation, ISAAC'98

Y2 - 14 December 1998 through 16 December 1998

ER -