ON STEINER MINIMAL-TREES WITH LP DISTANCE

CSpace

	ON STEINER MINIMAL-TREES WITH LP DISTANCE
	LIU, ZC; DU, DZ
	1992
发表期刊	ALGORITHMICA
ISSN	0178-4617
卷号	7 期号:2-3 页码:179-191
摘要	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.
关键词	STEINER TREES SPANNING TREES STEINER RATIO LP DISTANCE BOUNDS
语种	英语
WOS研究方向	Computer Science ; Mathematics
WOS类目	Computer Science, Software Engineering ; Mathematics, Applied
WOS记录号	WOS:A1992HA31400004
出版者	SPRINGER VERLAG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/27314
专题	中国科学院数学与系统科学研究院
通讯作者	LIU, ZC
作者单位	CHINESE ACAD SCI,INST APPL MATH,BEIJING,PEOPLES R CHINA
推荐引用方式 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.