KMS Of Academy of mathematics and systems sciences, CAS
ON BETTER HEURISTICS FOR STEINER MINIMUM TREES | |
DU, DZ; ZHANG, YJ | |
1992-11-02 | |
Source Publication | MATHEMATICAL PROGRAMMING |
ISSN | 0025-5610 |
Volume | 57Issue:2Pages:193-202 |
Abstract | Finding a shortest network interconnecting a given set of points in a metric space is called the Steiner minimum tree problem. The Steiner ratio is the largest lower bound for the ratio between lengths of a Steiner minimum tree and a minimum spanning tree for the same set of points. In this paper, we show that in a metric space, if the Steiner ratio is less than one and finding a Steiner minimum tree for a set of size bounded by a fixed number can be performed in polynomial time, then there exists a polynomial-time heuristic for the Steiner minimum tree problem with performance ratio bigger than the Steiner ratio. It follows that in the Euclidean plane, there exists a polynomial-time heuristic for Steiner minimum trees with performance ratio bigger than 1/2 square-root 3. This solves a long-standing open problem. |
Keyword | STEINER TREES APPROXIMATION PERFORMANCE RATIO |
Language | 英语 |
WOS Research Area | Computer Science ; Operations Research & Management Science ; Mathematics |
WOS Subject | Computer Science, Software Engineering ; Operations Research & Management Science ; Mathematics, Applied |
WOS ID | WOS:A1992KE27800004 |
Publisher | ELSEVIER SCIENCE BV |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/27692 |
Collection | 中国科学院数学与系统科学研究院 |
Affiliation | 1.CHINESE ACAD SCI,INST APPL MATH,BEIJING,PEOPLES R CHINA 2.SO METHODIST UNIV,DEPT COMP SCI,DALLAS,TX 75275 |
Recommended Citation GB/T 7714 | DU, DZ,ZHANG, YJ. ON BETTER HEURISTICS FOR STEINER MINIMUM TREES[J]. MATHEMATICAL PROGRAMMING,1992,57(2):193-202. |
APA | DU, DZ,&ZHANG, YJ.(1992).ON BETTER HEURISTICS FOR STEINER MINIMUM TREES.MATHEMATICAL PROGRAMMING,57(2),193-202. |
MLA | DU, DZ,et al."ON BETTER HEURISTICS FOR STEINER MINIMUM TREES".MATHEMATICAL PROGRAMMING 57.2(1992):193-202. |
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