A new approach to the maximum-flow problem
Journal of the ACM (JACM)
Combinatorial algorithms for integrated circuit layout
Combinatorial algorithms for integrated circuit layout
An efficient K-way graph partitioning algorithm for task allocation in parallel computing systems
ISCI '90 Proceedings of the first international conference on systems integration on Systems integration '90
Computing edge-connectivity in multigraphs and capacitated graphs
SIAM Journal on Discrete Mathematics
An Õ(n2) algorithm for minimum cuts
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
A polynomial algorithm for the k-cut problem for fixed k
Mathematics of Operations Research
A faster algorithm for finding the minimum cut in a directed graph
SODA selected papers from the third annual ACM-SIAM symposium on Discrete algorithms
A new approach to the minimum cut problem
Journal of the ACM (JACM)
Minimum cuts in near-linear time
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Computing All Small Cuts in an Undirected Network
SIAM Journal on Discrete Mathematics
Faster shortest-path algorithms for planar graphs
Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
A note on minimizing submodular functions
Information Processing Letters
On Minimum 3-Cuts and Approximating k-Cuts Using Cut Trees
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
Suboptimal Cuts: Their Enumeration, Weight and Number (Extended Abstract)
ICALP '92 Proceedings of the 19th International Colloquium on Automata, Languages and Programming
Beyond the flow decomposition barrier
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
A faster algorithm for computing minimum 5-way and 6-way cuts in graphs
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
A new and improved algorithm for the 3-cut problem
Operations Research Letters
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For an edge-weighted graph G with n vertices and m edges, we present a new deterministic algorithm for computing a minimum k-way cut for k = 3, 4. The algorithm runs in O(nk-2(nF(n,m) + C2(n,m) + n2)) = O(mnk log(n2/m)) time for k = 3, 4, where F(n,m) and C2(n,m) denote respectively the time bounds required to solve the maximum flow problem and the minimum 2-way cut problem in G. The bound for k = 3 matches the current best deterministic bound Õ(mn3) for weighted graphs, but improves the bound Õ(mn3) to Õ(n(nF(n,m) + C2(n,m) + n2)) = O(min{mn8/3, m3/2n2}) for unweighted graphs. The bound Õ(mn4) for k = 4 improves the previous best randomized bound Õ(n6) (for m = o(n2)). The algorithm is then generalized to the problem of finding a minimum 3-way cut in a symmetric submodular system.