II< This f{',search was sUr'rlOrleO in pan by Ih~Naj(lr.:al Scien..f' : FOl~"C'l1jon nnrkr G:J'1'nr~MCS-8201083 and DCR-83Z0124.

No abstract

Depart.ment. of Comput.er Sciences Purdue University West Lafayette. IN 47907 • This re9carch "11.9 supported in part by the National Science Foundation under Grant IlCS-6201063.

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.

No abstract