Minimum cost subpartitions in graphs
Information Processing Letters
Minimum k-way cuts via deterministic greedy tree packing
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Efficient Algorithms for the k Smallest Cuts Enumeration
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Divide-and-Conquer Algorithms for Partitioning Hypergraphs and Submodular Systems
ISAAC '09 Proceedings of the 20th 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
A polynomial-time approximation scheme for planar multiway cut
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Computing minimum multiway cuts in hypergraphs from hypertree packings
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
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Let $G=(V,E)$ be an edge-weighted undirected graph with $n$ vertices and $m$ edges. We present a deterministic algorithm to compute a minimum $k$-way cut of $G$ for a given $k$. Our algorithm is a divide-and-conquer method based on a procedure that reduces an instance of the minimum $k$-way cut problem to $O(n^{2k-5})$ instances of the minimum $(\lfloor (k+\sqrt{k})/2\rfloor+1)$-way cut problem, and can be implemented to run in $O(n^{4k/(1-1.71/\sqrt{k}) -31} )$ time. With a slight modification, the algorithm can find all minimum $k$-way cuts in $O(n^{4k/(1-1.71/\sqrt{k}) -16} )$ time.