Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
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
Approximation algorithms for graph augmentation
Journal of Algorithms
Data structures for weighted matching and nearest common ancestors with linking
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Discrete Applied Mathematics - Special issue: Special issue devoted to the fifth annual international computing and combinatories conference (COCOON'99) Tokyo, Japan 26-28 July 1999
Spanning Trees with Bounded Number of Branch Vertices
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
APPROX '01/RANDOM '01 Proceedings of the 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems and 5th International Workshop on Randomization and Approximation Techniques in Computer Science: Approximation, Randomization and Combinatorial Optimization
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Given an undirected, 2-edge-connected, and real weighted graph G, with n vertices and m edges, and given a spanning tree T of G, the 2-edge-connectivity augmentation problem with respect to G and T consists of finding a minimum-weight set of edges of G whose addition to T makes it 2-edge-connected While the general problem is NP-hard, in this paper we prove that it becomes polynomial time solvable if T can be rooted in such a way that a prescribed topological condition with respect to G is satisfied In such a case, we provide an ${\mathcal O}(n(m+h+\delta^{3}))$ time algorithm for solving the problem, where h and δ are the height and the maximum degree of T, respectively A faster version of our algorithm can be used for 2-edge connecting a spider tree, that is a tree with at most one vertex of degree greater than two This finds application in strengthening the reliability of optical networks.