A fast algorithm for optimally increasing the edge-connectivity

• Published in: Foundations of Computer Science, 31st Symposium pp. 698 - 707 vol.2
• Main Authors: Naor, D., Gusfield, D., Martel, C.
• Format: Conference Proceeding
• Language: English
• Published: IEEE Comput. Soc. Press 1990
• Subjects: Computer science; Data security; Graph theory; NP-hard problem; Polynomials
• ISBN: 081862082X; 9780818620829
• DOI: 10.1109/FSCS.1990.89592

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.< >