Steiner Trees on Sets of Three Points in λ-Geometry (λ=3m)

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概要

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• We show a method to determine a Steiner Minimum Tree (SMT) and a necessary and sufficient condition that an SMT is a full Steiner tree for three given points in λ-geometry (λ=3m, mis a positive integer). The λ-geometry allows only orientations with angles iπ/λ (i and λ (λ ⪯ 2) are integers), and fill up the gap between the rectilinear geometry (λ=2) and the Euclidean geometry (λ=∞). An SMT in λ-geometry (λ=3m) has a similar property to that in the Euclidean geometry. The method to determine an SMT in λ-geometry is an extension of the well-known method in the Euclidean geometry. The Steiner point in λ-geometry is any point in the intersection area with a parallelogram and a Steiner locus. Then there are infinite candidate locations of the Steiner point. The Steiner point in the Euclidean geometry is that in λ-geometry (λ=3m).

• 社団法人電子情報通信学会の論文
• 2002-08-01

著者

• HAYASE Michiyoshi

  Faculty of Computer Science and System Engineering, Okayama Prefectural University

• Hayase M

  Faculty Of Computer Science And System Engineering Okayama Prefectural University

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• Steiner Trees on Sets of Three Points in λ-Geometry (λ=3m)

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