SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
A 5/4-approximation algorithm for minimum 2-edge-connectivity
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Hardness of Approximation for Vertex-Connectivity Network-Design Problems
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Special edges, and approximating the smallest directed k-edge connected spanning subgraph
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithm for k-node connected subgraphs via critical graphs
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Approximating the smallest k-edge connected spanning subgraph by LP-rounding
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Iterated rounding algorithms for the smallest k-edge connected spanning subgraph
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
An o(log2 k)-approximation algorithm for the k-vertex connected spanning subgraph problem
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
On k-connectivity problems with sharpened triangle inequality
Journal of Discrete Algorithms
Parameterizing above or below guaranteed values
Journal of Computer and System Sciences
An almost O(log k)-approximation for k-connected subgraphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
On k-edge-connectivity problems with sharpened triangle inequality
CIAC'03 Proceedings of the 5th Italian conference on Algorithms and complexity
Approximability and inapproximability of the minimum certificate dispersal problem
Theoretical Computer Science
Approximating survivable networks with β-metric costs
Journal of Discrete Algorithms
Approximating the smallest 2-vertex connected spanning subgraph of a directed graph
ESA'11 Proceedings of the 19th European conference on Algorithms
On the maximum size of a minimal k-edge connected augmentation
Journal of Combinatorial Theory Series B
Approximation algorithms for the minimum cardinality two-connected spanning subgraph problem
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Iterated Rounding Algorithms for the Smallest k-Edge Connected Spanning Subgraph
SIAM Journal on Computing
A rounding by sampling approach to the minimum size k-arc connected subgraph problem
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
A 4/3-approximation algorithm for minimum 3-edge-connectivity
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Small ℓ-edge-covers in k-connected graphs
Discrete Applied Mathematics
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An efficient heuristic is presented for the problem of finding a minimum-size k-connected spanning subgraph of an (undirected or directed) simple graph G=(V,E). There are four versions of the problem, and the approximation guarantees are as follows:minimum-size k-node connected spanning subgraph of an undirected graph 1 + [1/k], minimum-size k-node connected spanning subgraph of a directed graph 1 + [1/k], minimum-size k-edge connected spanning subgraph of an undirected graph 1+[2/(k+1)], minimum-size k-edge connected spanning subgraph of a directed graph 1 + [4/\sqrt{k}]. The heuristic is based on a subroutine for the degree-constrained subgraph (b-matching) problem. It is simple and deterministic and runs in time O(k|E|2).The following result on simple undirected graphs is used in the analysis: The number of edges required for augmenting a graph of minimum degree k to be k-edge connected is at most k,|V|/(k+1).For undirected graphs and k=2, a (deterministic) parallel NC version of the heuristic finds a 2-node connected (or 2-edge connected) spanning subgraph whose size is within a factor of ($1.5+\epsilon$) of minimum, where $\epsilon0$ is a constant.