Jump to Content
Your Recent History
View Cart
Logged Out Log In
SIAM J. Discrete Math. 21, pp. 612-636 (25 pages)
Approximation Algorithms for Network Design with Metric Costs
Alerts
Alert Me When Cited
Alert Me When Corrected
Tools
Download Citation
Add to MyScitation
Blog This Article
Print-Friendly
Research Toolkit
Share
Email Abstract
Connotea
CiteULike
del.icio.us
BibSonomy
Tweet this Article
Add to FacebookWe study undirected networks with edge costs that satisfy the triangle inequality. Let $n$ denote the number of nodes. We present an $O(1)$-approximation algorithm for a generalization of the metric-cost subset $k$-node-connectivity problem. Our approximation guarantee is proved via lower bounds that apply to the simple edge-connectivity version of the problem, where the requirements are for edge-disjoint paths rather than for openly node-disjoint paths. A corollary is that, for metric costs and for each $k=1,2,\dots,n-1$, there exists a $k$-node connected graph whose cost is within a factor of ${ 22\/}$ of the cost of any simple $k$-edge connected graph. Based on our $O(1)$-approximation algorithm, we present an $O(\log r_{\max})$-approximation algorithm for the metric-cost node-connectivity survivable network design problem, where $r_{\max}$ denotes the maximum requirement over all pairs of nodes. Our results contrast with the case of edge costs of 0 or 1, where Kortsarz, Krauthgamer, and Lee. [SIAM J. Comput., 33 (2004), pp. 704–720] recently proved, assuming NP$\nsubseteq\;$DTIME($n^{polylog(n)}$), a hardness-of-approximation lower bound of $2^{\log^{1-\epsilon}n}$ for the subset $k$-node-connectivity problem, where $\epsilon$ denotes a small positive number.
© 2007 Society for Industrial and Applied Mathematics
RELATED DATABASES
To view database links for this article,
you need to log in.
KEYWORDS
PUBLICATION DATA
ARTICLE DATA
History
Received December 30, 2004
Accepted January 18, 2007
Published online July 25, 2007
Accepted January 18, 2007
Published online July 25, 2007
Digital Object Identifier
For access to fully linked references, you need to log in.
For access to citing articles, you need to log in.
ALL SIAM Content
Scitation
Google Scholar