A polynomial algorithm for the k-cut problem for fixed k
Mathematics of Operations Research
The Complexity of Multiterminal Cuts
SIAM Journal on Computing
Beyond the flow decomposition barrier
Journal of the ACM (JACM)
Rounding algorithms for a geometric embedding of minimum multiway cut
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
An improved approximation algorithm for MULTIWAY CUT
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
A simple algorithm for the planar multiway cut problem
Journal of Algorithms
A 2-Approximation Algorithm for the Directed Multiway Cut Problem
SIAM Journal on Computing
Multiway cuts in node weighted graphs
Journal of Algorithms
Multicuts in unweighted graphs and digraphs with bounded degree and bounded tree-width
Journal of Algorithms
The Closest Substring problem with small distances
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Finding small balanced separators
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Parameterized graph separation problems
Theoretical Computer Science - Parameterized and exact computation
Complexity and exact algorithms for multicut
SOFSEM'06 Proceedings of the 32nd conference on Current Trends in Theory and Practice of Computer Science
An improved parameterized algorithm for the minimum node multiway cut problem
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Constant ratio fixed-parameter approximation of the edge multicut problem
Information Processing Letters
Fixed-parameter tractability of multicut parameterized by the size of the cutset
Proceedings of the forty-third annual ACM symposium on Theory of computing
Slightly superexponential parameterized problems
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Important separators and parameterized algorithms
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
FPT algorithms for path-transversal and cycle-transversal problems
Discrete Optimization
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Given a graph G = (V, E) with n vertices and m edges, and a subset T of l vertices called terminals, the Edge (respectively, Vertex) Multiterminal Cut problem is to find a set of k edges (nonterminal vertices), whose removal from G separates each terminal from all the others. These two problems are NP-hard for l ≥ 3 but well-known to be polynomial-time solvable for l = 2 by the flow technique. In this paper, we show that Edge Multiterminal Cut is polynomial-time solvable for k = O(log n) by presenting an O(2klT (n, m)) algorithm, where T(n, m) = O(min(n2/3, m1/2)m) is the running time of finding a minimum (s, t) cut in an unweighted graph. We also give two algorithms for Vertex Multiterminal Cut that run in O(lkT(n, m)) time and O((k!)2T(n, m)) time respectively. The former one indicates that Vertex Multiterminal Cut is solvable in polynomial time for l being a constant and k = O(log n), and the latter one improves the best known algorithm of running time O(4k3 nO(1)). When l = 3, we show that the running times can be improved to O(1.415kT(n, m)) for Edge Multiterminal Cut and O(2.059kT(n, m)) for Vertex Multiterminal Cut. Furthermore, we present a simple idea to solve another important problem Multicut by finding minimum multiterminal cuts. Our algorithms for Multicuts are also faster than the previously best algorithm. Based on a notion farthest minimum isolating cut, we present some properties for Multiterminal Cuts, which help shed light on the structure of optimal cut problems, and enables us to design efficient algorithms for Multiterminal Cuts, as well as some other related cut problems.