Proceedings  31st Annual Symposium on Foundations of Computer Science (1990)
St. Louis, MO, USA
Oct. 22, 1990 to Oct. 24, 1990
pp: 698-707 vol.2
D. Naor , Div. of Comput. Sci., California Univ., Davis, CA, USA
D. Gusfield , Div. of Comput. Sci., California Univ., Davis, CA, USA
C. Martel , Div. of Comput. Sci., California Univ., Davis, CA, USA
An undirected, unweighted graph G=(V, E with n nodes, m edges, and connectivity lambda ) is considered. Given an input parameter delta , the edge augmentation problem is to find the smallest set of edges to add to G so that its edge-connectivity is increased by delta . A solution to this problem that runs in time O( delta /sup 2/nm+nF(n)), where F(n) is the time to perform one maximum flow on G, is given. The solution gives the optimal augmentation for every delta ', 1<or= delta '<or= delta , in the same time bound. A modification of the solution solves the problem without knowing delta in advance. If delta =1, then the solution is particularly simple, running in O(nm) time, and it is a natural generalization of an algorithm of K. Eswaran and R.E. Tarjan (1976) for the case in which lambda + delta =2. The converse problem (given an input number k, increase the connectivity of G as much as possible by adding at most k edges) is solved in the same time bound. The solution makes extensive use of the structure of particular sets of cuts.
time bound, undirected unweighted graph, time complexity, edge-connectivity, input parameter, edge augmentation problem, optimal augmentation
C. Martel, D. Naor and D. Gusfield, "A fast algorithm for optimally increasing the edge-connectivity," Proceedings  31st Annual Symposium on Foundations of Computer Science(FOCS), St. Louis, MO, USA, 1990, pp. 698-707 vol.2.