Edge-connectivity augmentation problems
Journal of Computer and System Sciences
Parallel ear decomposition search (EDS) and st-numbering in graphs
Theoretical Computer Science
A matroid approach to finding edge connectivity and packing arborescences
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Fully dynamic algorithms for edge connectivity problems
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Algorithms for parallel k-vertex connectivity and sparse certificates
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Approximation algorithms for graph augmentation
Approximation algorithms for graph augmentation
A linear time algorithm for triconnectivity augmentation (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Ambivalent data structures for dynamic 2-edge-connectivity and k smallest spanning trees
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Applications of a poset representation to edge connectivity and graph rigidity
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
On finding minimal 2-connected subgraphs
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Biconnectivity approximations and graph carvings
Biconnectivity approximations and graph carvings
Computing minimal spanning subgraphs in linear time
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Improved approximations for the Steiner tree problem
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Survivable networks, linear programming relaxations and the parsimonious property
Mathematical Programming: Series A and B
Journal of the ACM (JACM)
Graph Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On Finding a Smallest Augmentation to Biconnect a Graph
ISA '91 Proceedings of the 2nd International Symposium on Algorithms
Random sampling in cut, flow, and network design problems
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Improved approximation algorithms for biconnected subgraphs via better lower bounding techniques
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Approximating the minimum equivalent digraph
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
A scaling technique for better network design
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Power optimization in fault-tolerant topology control algorithms for wireless multi-hop networks
IEEE/ACM Transactions on Networking (TON)
k-edge-connectivity: approximation and LP relaxation
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
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A spanning tree in a graph is the smallest connected spanning subgraph. Given a graph, how does one find the smallest (i.e., least number of edges) 2-connected spanning subgraph (connectivity refers to both edge and vertex connectivity, if not specified)? Unfortunately, the problem is known to be NP-hard.We consider the problem of finding an approximation to the smallest 2-connected subgraph, by an efficient algorithm. For 2-edge connectivity our algorithm guarantees a solution that is no more than 3/2 times the optimal. For 2-vertex connectivity our algorithm guarantees a solution that is no more than 5/3 times the optimal. The previous best approximation factor is 2 for each of these problems. The new algorithms (and their analyses) depend upon a structure called a carving of a graph, which is of independent interest. We show that approximating the optimal solution to within an additive constant is NP-hard as well.We also consider the case where the graph has edge weights. We show that an approximation factor of 2 is possible in polynomial time for finding a k-edge connected spanning subgraph. This improves an approximation factor of 3 for k=2 due to [FJ81], and extends it for any k (with an increased running time though).