Biconnectivity approximations and graph carvings
Journal of the ACM (JACM)
Handbook of combinatorics (vol. 1)
Handbook of combinatorics (vol. 1)
Improved approximation algorithms for biconnected subgraphs via better lower bounding techniques
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Improved approximation algorithms for network design problems
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
A New Bound for the 2-Edge Connected Subgraph Problem
Proceedings of the 6th International IPCO Conference on Integer Programming and Combinatorial Optimization
An approximation scheme for planar graph TSP
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
A Factor 2 Approximation Algorithm for the Generalized Steiner Network Problem
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
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
Finding 2-edge connected spanning subgraphs
Operations Research Letters
| Hi-index | 0.01 |
We study some versions of the problem of finding the minimum size 2-connected subgraph. This problem is NP-hard (even on cubic planar graphs) and MAX SNP-hard. We show that the minimum 2-edge connected subgraph problem can be approximated to within 4/3-Ɛ for general graphs, improving upon the recent result of Vempala and Vetta [14]. Better approximations are obtained for planar graphs and for cubic graphs.We also consider the generalization, where requirements of 1 or 2 edge or vertex disjoint paths are specified between every pair of vertices, and the aim is to find a minimum subgraph satisfying these requirements. We show that this problem can be approximated within 3/2, generalizing earlier results for 2-connectivity. We also analyze the classical local optimization heuristics. For cubic graphs, our results imply a new upper bound on the integrality gap of the linear programming formulation for the 2-edge connectivity problem.