A new approach to the maximum-flow problem
Journal of the ACM (JACM)
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
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
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 new and improved algorithm for the 3-cut problem
Operations Research Letters
A Fast Algorithm for Computing Minimum 3-Way and 4-Way Cuts
Proceedings of the 7th International IPCO Conference on Integer Programming and Combinatorial Optimization
Approximating the Minimum k-way Cut in a Graph via Minimum 3-way Cuts
ISAAC '99 Proceedings of the 10th International Symposium on Algorithms and Computation
Finding minimum 3-way cuts in hypergraphs
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Finding minimum 3-way cuts in hypergraphs
Information Processing Letters
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For an edge-weighted graph G with n vertices and m edges, the minimum k-way cut problem is to find a partition of the vertex set into k non-empty subsets so that the weight sum of edges between different subsets is minimized. For this problem with k = 5 and 6, we present a deterministic algorithm that runs in O(nk-2(nF(n;m) + C2(n, m) + n2)) = O(mnk log(n2/m)) time, 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 bounds Õ(mn5) for k = 5 and Õ(mn6) for k = 6 improve the previous best randomized bounds Õ(n8) and Õ(n10), respectively.