The steiner tree problem in λ4-geometry plane

Guo Hui Lin; Guoliang Xue

doi:10.1007/3-540-49381-6_35

The steiner tree problem in λ₄-geometry plane

Guo Hui Lin, Guoliang Xue

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

5 Scopus citations

Abstract

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 G_{n - 2}.

Original language	English (US)
Title of host publication	Algorithms and Computation - 9th International Symposium, ISAAC'98, Proceedings
Publisher	Springer Verlag
Pages	327-337
Number of pages	11
ISBN (Print)	3540653856, 9783540653851
DOIs	https://doi.org/10.1007/3-540-49381-6_35
State	Published - 1998
Externally published	Yes
Event	9th Annual International Symposium on Algorithms and Computation, ISAAC'98 - Taejon, Korea, Republic of Duration: Dec 14 1998 → Dec 16 1998

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	1533 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	9th Annual International Symposium on Algorithms and Computation, ISAAC'98
Country/Territory	Korea, Republic of
City	Taejon
Period	12/14/98 → 12/16/98

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/3-540-49381-6_35

Cite this

Lin, G. H., & Xue, G. (1998). The steiner tree problem in λ₄-geometry plane. In Algorithms and Computation - 9th International Symposium, ISAAC'98, Proceedings (pp. 327-337). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1533 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-49381-6_35

The steiner tree problem in λ₄-geometry plane. / Lin, Guo Hui; Xue, Guoliang.
Algorithms and Computation - 9th International Symposium, ISAAC'98, Proceedings. Springer Verlag, 1998. p. 327-337 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1533 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Lin, GH & Xue, G 1998, The steiner tree problem in λ₄-geometry plane. in Algorithms and Computation - 9th International Symposium, ISAAC'98, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1533 LNCS, Springer Verlag, pp. 327-337, 9th Annual International Symposium on Algorithms and Computation, ISAAC'98, Taejon, Korea, Republic of, 12/14/98. https://doi.org/10.1007/3-540-49381-6_35

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