How to cut a graph into many pieces
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
An FPT algorithm for edge subset feedback edge set
Information Processing Letters
Fixed-parameter tractability of directed multiway cut parameterized by the size of the cutset
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Multicut algorithms via tree decompositions
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
On multiway cut parameterized above lower bounds
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
On multiway cut parameterized above lower bounds
ACM Transactions on Computation Theory (TOCT)
Finding small separators in linear time via treewidth reduction
ACM Transactions on Algorithms (TALG)
An o *(1.84 k) parameterized algorithm for the multiterminal cut problem
FCT'13 Proceedings of the 19th international conference on Fundamentals of Computation Theory
An O*(1.84k) parameterized algorithm for the multiterminal cut problem
Information Processing Letters
On the generalized multiway cut in trees problem
Journal of Combinatorial Optimization
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Given a graph G=(V,E) with n vertices and m edges, and a subset T of k vertices called terminals, the Edge (respectively, Vertex) Multiterminal Cut problem is to find a set of at most l edges (non-terminal vertices), whose removal from G separates each terminal from all the others. These two problems are NP-hard for k≥3 but well-known to be polynomial-time solvable for k=2 by the flow technique. In this paper, based on a notion farthest minimum isolating cut, we design several simple and improved algorithms for Multiterminal Cut. We show that Edge Multiterminal Cut can be solved in O(2 l kT(n,m)) time and Vertex Multiterminal Cut can be solved in O(k l T(n,m)) time, where T(n,m)=O(min (n 2/3,m 1/2)m) is the running time of finding a minimum (s,t) cut in an unweighted graph. Furthermore, the running time bounds of our algorithms can be further reduced for small values of k: Edge 3-Terminal Cut can be solved in O(1.415 l T(n,m)) time, and Vertex {3,4,5,6}-Terminal Cuts can be solved in O(2.059 l T(n,m)), O(2.772 l T(n,m)), O(3.349 l T(n,m)) and O(3.857 l T(n,m)) time respectively. Our results on Multiterminal Cut can also be used to obtain faster algorithms for Multicut: $O((\min(\sqrt{2k},l)+1)^{2k}2^{l}T(n,m))$-time algorithm for Edge Multicut and O((2k) k+l/2 T(n,m))-time algorithm for Vertex Multicut.