A note on Rooted Survivable Networks
Information Processing Letters
Approximating survivable networks with β-metric costs
Journal of Discrete Algorithms
An improved approximation algorithm for minimum-cost subset k-connectivity
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Degree Bounded Network Design with Metric Costs
SIAM Journal on Computing
Approximating subset k-connectivity problems
WAOA'11 Proceedings of the 9th international conference on Approximation and Online Algorithms
Approximating minimum-cost connectivity problems via uncrossable bifamilies
ACM Transactions on Algorithms (TALG)
Approximating subset k-connectivity problems
Journal of Discrete Algorithms
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We 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.