Biconnectivity approximations and graph carvings
Journal of the ACM (JACM)
Approximation algorithms for finding highly connected subgraphs
Approximation algorithms for NP-hard problems
Improved approximation algorithms for biconnected subgraphs via better lower bounding techniques
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
On approximability of the minimum-cost k-connected spanning subgraph problem
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A 5/4-approximation algorithm for minimum 2-edge-connectivity
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Factor 4/3 approximations for minimum 2-connected subgraphs
APPROX '00 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization
Hardness of Approximation for Vertex-Connectivity Network-Design Problems
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
Some complexity results for the Traveling Salesman Problem
STOC '76 Proceedings of the eighth annual ACM symposium on Theory of computing
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Finding a minimum size 2-vertex connected spanning subgraph of a k-vertex connected graph G = (V,E) with n vertices and m edges is known to be NP-hard and APX-hard, as well as approximable in O(n2m) time within a factor of 4/3. Interestingly, the problem remains NP-hard even if a Hamiltonian path of G is given as part of the input. For this input-enriched version of the problem, we provide in this paper a linear time and space algorithm which approximates the optimal solution by a factor of no more than min ${\{\frac{5}{4},\frac{2k-1}{2(k-1)}\}}$.