Theoretical Efficiency of the Edmonds-Karp Algorithm for Computing Maximal Flows
Journal of the ACM (JACM)
Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems
Journal of the ACM (JACM)
Algorithm 447: efficient algorithms for graph manipulation
Communications of the ACM
An Algorithm for Determining Whether the Connectivity of a Graph is at Least k
An Algorithm for Determining Whether the Connectivity of a Graph is at Least k
An efficient implementation of Edmonds'' maximum matching algorithm.
An efficient implementation of Edmonds'' maximum matching algorithm.
On the complexity of edge traversing
Journal of the ACM (JACM)
The Effect of a Connectivity Requirement on the Complexity of Maximum Subgraph Problems
Journal of the ACM (JACM)
The subgraph homeomorphism problem
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Node-and edge-deletion NP-complete problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Building connected neighborhood graphs for isometric data embedding
Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining
Building k-Connected Neighborhood Graphs for Isometric Data Embedding
IEEE Transactions on Pattern Analysis and Machine Intelligence
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An algorithm proposed by Dinic for finding maximum flows in networks and by Hopcroft and Karp for finding maximum bipartite matchings is applied to graph connectivity problems. It is shown that the algorithm requires 0(V1/2E) time to find a maximum set of node-disjoint paths in a graph, and 0(V2/3E) time to find a maximum set of edge disjoint paths. These bounds are tight. Thus the node connectivity of a graph may be tested in 0(V5/2E) time, and the edge connectivity of a graph may be tested in 0(V5/3E) time.