KMS Of Academy of mathematics and systems sciences, CAS
ON STEINER MINIMAL-TREES WITH LP DISTANCE | |
LIU, ZC; DU, DZ | |
1992 | |
Source Publication | ALGORITHMICA |
ISSN | 0178-4617 |
Volume | 7Issue:2-3Pages:179-191 |
Abstract | Let L(p) be the plane with the distance d(rho)(A1, A2) = ([x1 - X2[p + [y1 - y2[p)/1p where x(i) and y(i) are the cartesian coordinates of the point A(i). Let P be a finite set of points in L(p). We consider Steiner minimal trees on P. It is proved that, for 1 < p < infinity, each Steiner point is of degree exactly three. Define the Steiner ratio rho(p) to be inf{L(s)(P)/L(m)(P)[P subset-of L(p)} where L(s)(P) and L(m)(P) are lengths of the Steiner minimal tree and the minimal spanning tree on P, respectively. Hwang showed rho-1 = 2/3. Chung and Graham proved rho-2 > 0.842. We prove in this paper that rho(infinity) = 2/3 and square-root(square-root 2/2)rho-1-rho-2 less-than-or-equal-to rho(p) less-than-or-equal-to square-root 3/2 for any p. |
Keyword | STEINER TREES SPANNING TREES STEINER RATIO LP DISTANCE BOUNDS |
Language | 英语 |
WOS Research Area | Computer Science ; Mathematics |
WOS Subject | Computer Science, Software Engineering ; Mathematics, Applied |
WOS ID | WOS:A1992HA31400004 |
Publisher | SPRINGER VERLAG |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/27314 |
Collection | 中国科学院数学与系统科学研究院 |
Corresponding Author | LIU, ZC |
Affiliation | CHINESE ACAD SCI,INST APPL MATH,BEIJING,PEOPLES R CHINA |
Recommended Citation GB/T 7714 | LIU, ZC,DU, DZ. ON STEINER MINIMAL-TREES WITH LP DISTANCE[J]. ALGORITHMICA,1992,7(2-3):179-191. |
APA | LIU, ZC,&DU, DZ.(1992).ON STEINER MINIMAL-TREES WITH LP DISTANCE.ALGORITHMICA,7(2-3),179-191. |
MLA | LIU, ZC,et al."ON STEINER MINIMAL-TREES WITH LP DISTANCE".ALGORITHMICA 7.2-3(1992):179-191. |
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