Approximation algorithms for graph augmentation
Journal of 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
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
Hardness of Approximation for Vertex-Connectivity Network Design Problems
SIAM Journal on Computing
Parameterized Complexity
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Connectivity augmentation problems ask for adding a set of at most k edges whose insertion makes a given graph satisfy a specified connectivity property, such as bridge-connectivity or biconnectivity. We show that, for bridge-connectivity and biconnectivity, the respective connectivity augmentation problems admit problem kernels with O(k2) vertices and links. Moreover, we study partial connectivity augmentation problems, naturally generalizing connectivity augmentation problems. Here, we do not require that, after adding the edges, the entire graph should satisfy the connectivity property, but a large subgraph. In this setting, two polynomial-time solvable connectivity augmentation problems behave differently, namely, the partial biconnectivity augmentation problem remains polynomial-time solvable whereas the partial strong connectivity augmentation problem becomes W[2]-hard with respect to k.