Very simple methods for all pairs network flow analysis
SIAM Journal on Computing
Counterexamples for Directed and Node Capacitated Cut-Trees
SIAM Journal on Computing
A matroid approach to finding edge connectivity and packing arborescences
Selected papers of the 23rd annual ACM symposium on Theory of computing
Preserving and Increasing Local Edge-Connectivity in Mixed Graphs
SIAM Journal on Discrete Mathematics
Finding maximum flows in undirected graphs seems easier than bipartite matching
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Beyond the flow decomposition barrier
Journal of the ACM (JACM)
Cut tree algorithms: an experimental study
Journal of Algorithms
A fast algorithm for computing steiner edge connectivity
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Efficient algorithms for computing all low s-t edge connectivities and related problems
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Fast edge splitting and Edmonds' arborescence construction for unweighted graphs
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Fast edge orientation for unweighted graphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Communications of the ACM
Efficient edge splitting-off algorithms maintaining all-pairs edge-connectivities
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Fast matrix rank algorithms and applications
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Research paper: The saga of minimum spanning trees
Computer Science Review
Fast matrix rank algorithms and applications
Journal of the ACM (JACM)
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We present a fast algorithm for computing a Gomory-Hu tree or cut tree for an unweighted undirected graph G = (V,E). The expected running time of our algorithm is Õ(mc) where |E| = m and c is the maximum u-vedge connectivity, where u,v ∈ V. When the input graph is also simple (i.e., it has no parallel edges), then the u-v edge connectivity for each pair of vertices u and v is at most n-1; so the expected running time of our algorithm for simple unweighted graphs is Õ(mn). All the algorithms currently known for constructing a Gomory-Hu tree [8,9] use n-1 minimum s-t cut (i.e., max flow) subroutines. This in conjunction with the current fastest Õ(n20/9) max flow algorithm due to Karger and Levine [11] yields the current best running time of Õ(n20/9n) for Gomory-Hu tree construction on simpleunweighted graphs with m edges and n vertices. Thus we present the first Õ(mn) algorithm for constructing a Gomory-Hu tree for simple unweighted graphs.We do not use a max flow subroutine here; we present an efficient tree packing algorithm for computing Steiner edge connectivity and use this algorithm as our main subroutine. The advantage in using a tree packing algorithm for constructing a Gomory-Hu tree is that the work done in computing a minimum Steiner cut for a Steiner set S ⊆ V can be reused for computing a minimum Steiner cut for certain Steiner sets S' ⊆ S.