The steiner tree problem in λ4-geometry plane

Guo Hui Lin, Guoliang Xue

Research output: Chapter in Book/Report/Conference proceedingConference 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 Gn - 2.

Original languageEnglish (US)
Title of host publicationAlgorithms and Computation - 9th International Symposium, ISAAC'98, Proceedings
PublisherSpringer Verlag
Pages327-337
Number of pages11
ISBN (Print)3540653856, 9783540653851
DOIs
StatePublished - 1998
Externally publishedYes
Event9th Annual International Symposium on Algorithms and Computation, ISAAC'98 - Taejon, Korea, Republic of
Duration: Dec 14 1998Dec 16 1998

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1533 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other9th Annual International Symposium on Algorithms and Computation, ISAAC'98
CountryKorea, Republic of
CityTaejon
Period12/14/9812/16/98

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • 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