On Shortest k-Edge-Connected Steiner Networks in Metric Spaces

Xiufeng Du, Xiaodong Hu () and Xiaohua Jia ()

Journal of Combinatorial Optimization, 2000, vol. 4, issue 1, No 5, 99-107

Abstract: Abstract Given a set of points P in a metric space, let l(P) denote the ratio of lengths between the shortest k-edge-connected Steiner network and the shortest k-edge-connected spanning network on P, and let r = inf l(P) ∣ P for k ≥ 1. In this paper, we show that in any metric space, r ≥ 3/4 for k ≥ 2, and there exists a polynomial-time α-approximation for the shortest k-edge-connected Steiner network, where α = 2 for even k and α = 2 + 4/(3k) for odd k. In the Euclidean plane, $$r_k \geqslant \sqrt 3 /2,\;\;r_3 \leqslant (\sqrt 3 + 2)/4$$ and $$r_4 \leqslant (7 + 3\sqrt 3 )/(9 + 2\sqrt 3 )$$ .

Keywords: k-edge-connectivity; spanning networks; Steiner networks; Steiner ratio (search for similar items in EconPapers)
Date: 2000
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1023/A:1009889023408 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jcomop:v:4:y:2000:i:1:d:10.1023_a:1009889023408

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10878

DOI: 10.1023/A:1009889023408

Access Statistics for this article

Journal of Combinatorial Optimization is currently edited by Thai, My T.

More articles in Journal of Combinatorial Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().