Approximation Algorithms for Several Graph Augmentation Problems
Greg N. Frederickson, Joseph F. JáJá · SIAM Journal on Computing · 1981
Graph augmentation problems on a weighted graph involve determining a minimum-cost set of edges to add to a graph to satisfy a specified property, such as biconnectivity, bridge-connectivity or strong connectivity. These augmentation problems are shown to be NP-complete in the restricted case of the graph being initially connected. Approximation algorithms with favorable time complexity are presented and shown to have constant worst-case performance ratios.