An almost O(log k)-approximation for k-connected subgraphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Inapproximability of survivable networks
Theoretical Computer Science
Online and stochastic survivable network design
Proceedings of the forty-first annual ACM symposium on Theory of computing
A Graph Reduction Step Preserving Element-Connectivity and Applications
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
A note on Rooted Survivable Networks
Information Processing Letters
Approximating Node-Connectivity Augmentation Problems
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Tree embeddings for two-edge-connected network design
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Approximating survivable networks with minimum number of Steiner points
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
Approximating survivable networks with β-metric costs
Journal of Discrete Algorithms
Approximability of capacitated network design
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
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
Approximating rooted Steiner networks
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Approximating fault-tolerant group-Steiner problems
Theoretical Computer Science
Survivable network activation problems
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Approximating minimum-cost connectivity problems via uncrossable bifamilies
ACM Transactions on Algorithms (TALG)
Survivable network activation problems
Theoretical Computer Science
| Hi-index | 0.00 |
In the Survivable Network Design Problem (SNDP) the goal is tofind a minimum cost subset of edges that satisfies a given set ofpairwise connectivity requirements among the vertices. Thisgeneral network design framework has been studied extensively andis tied to the development of major algorithmic techniques. Forthe edge-connectivity version of the problem, a $2$-approximationalgorithm is known for arbitrary pairwise connectivityrequirements. However, no non-trivial algorithms are known for itsvertex connectivity counterpart. In fact, even highly restrictedspecial cases of the vertex connectivity version remain poorlyunderstood.We study the single-source $k$-vertex connectivity version ofSNDP. We are given a graph $G(V,E)$ with a subset $T$ of terminalsand a source vertex $s$, and the goal is to find a minimum costsubset of edges ensuring that every terminal is $k$-vertexconnected to $s$. Our main result is an $O(k \log n)$-approximation algorithm for this problem; this improves uponthe recent $2^{O(k^2)}\log^4n$-approximation. Our algorithm isbased on an intuitive rerouting scheme. The analysis relies on astructural result that may be of independent interest: we showthat any solution can be decomposed into a disjoint collection ofmultiple-legged spiders, which are then used to re-route flow fromterminals to the source via other terminals.We also obtain the first non-trivial approximation algorithm forthe vertex-cost version of the same problem, achieving an $O(k^7 \log^2 n)$-approximation.