A polynomial algorithm for the k-cut problem for fixed k
Mathematics of Operations Research
The Complexity of Multiterminal Cuts
SIAM Journal on Computing
Multiway cuts in node weighted graphs
Journal of Algorithms
Parameterized graph separation problems
Theoretical Computer Science - Parameterized and exact computation
A fixed-parameter algorithm for the directed feedback vertex set problem
Journal of the ACM (JACM)
Algorithmic Aspects of Graph Connectivity
Algorithmic Aspects of Graph Connectivity
Simple and Improved Parameterized Algorithms for Multiterminal Cuts
Theory of Computing Systems - Special Issue: Symposium on Computer Science; Guest Editors: Sergei Artemov, Volker Diekert and Alexander Razborov
Exact Exponential Algorithms
Proceedings of the forty-third annual ACM symposium on Theory of computing
Fixed-parameter tractability of multicut parameterized by the size of the cutset
Proceedings of the forty-third annual ACM symposium on Theory of computing
Approximation Algorithms for Submodular Multiway Partition
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
The Minimum k-way Cut of Bounded Size is Fixed-Parameter Tractable
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
A polynomial-time approximation scheme for planar multiway cut
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Solving planar k-terminal cut in O(nc√k) time
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
A tight lower bound for planar multiway cut with fixed number of terminals
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
On multiway cut parameterized above lower bounds
ACM Transactions on Computation Theory (TOCT)
Simplex partitioning via exponential clocks and the multiway cut problem
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We study the multiterminal cut problem, which, given an n-vertex graph whose edges are integer-weighted and a set of terminals, asks for a partition of the vertex set such that each terminal is in a distinct part, and the total weight of crossing edges is at most k. Our weapons shall be two classical results known for decades. One is max volume min (s,t)-cuts by [Ford and Fulkerson, Flows in Networks. Princeton University Press, 1962], and the other is isolating cuts by [Dahlhaus et al., The complexity of multiterminal cuts. SIAM J. Comp. 23(4), 1994]. We sharpen these old weapons with the help of submodular functions, and apply them to this problem, which enable us to design a more elaborated branching scheme on deciding whether a non-terminal vertex is with a terminal or not. This bounded search tree algorithm can be shown to run in $1.84^k\cdot n^{{\cal O}(1)}$, thereby breaking the $2^k\cdot n^{{\cal O}(1)}$ barrier. As a by-product, it gives a $1.36^k\cdot n^{{\cal O}(1)}$ algorithm for 3-terminal cut. The preprocessing applied on non-terminal vertices might be of use for study of this problem from other aspects.