Edge-connectivity augmentation problems
Journal of Computer and System Sciences
Applications of a poset representation to edge connectivity and graph rigidity
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Augmenting graphs to meet edge-connectivity requirements
SIAM Journal on Discrete Mathematics
Approximation algorithms for graph augmentation
Journal of Algorithms
Biconnectivity approximations and graph carvings
Journal of the ACM (JACM)
Approximation algorithms for finding highly connected subgraphs
Approximation algorithms for NP-hard problems
Worst-case efficient priority queues
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
A Faster Approximation Algorithm for 2-Edge-Connectivity Augmentation
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
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Given a graph G of n vertices and m edges, and given a spanning subgraph H of G, the problem of finding a minimum weight set of edges of G, denoted as AUG2(H,G), to be added to H to make it 2-edge connected, is known to be NP-hard. In this paper, we present polynomial time efficient algorithms for solving the special case of this classic augmentation problem in which the subgraph H is a Hamiltonian path of G. More p recisely, we show that if G is unweighted, then AUG2(H,G) can be computed in O(m) time and space, while if G is nonnegatively weighted, then AUG2(H,G) can be computed in O(m+n log n) time and O(m) space. These results have an interesting application for solving a survivability problem on communication networks.