The Complexity of Multiterminal Cuts
SIAM Journal on Computing
On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Approximate Max-Flow Min-(Multi)Cut Theorems and Their Applications
SIAM Journal on Computing
Improved results for directed multicut
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Cutting and Partitioning a Graph aifter a Fixed Pattern (Extended Abstract)
Proceedings of the 10th Colloquium on Automata, Languages and Programming
Splitters and near-optimal derandomization
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Multicuts in unweighted graphs and digraphs with bounded degree and bounded tree-width
Journal of Algorithms
Machine Learning
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized graph separation problems
Theoretical Computer Science - Parameterized and exact computation
ON THE HARDNESS OF APPROXIMATING MULTICUT AND SPARSEST-CUT
Computational Complexity
Correlation clustering in general weighted graphs
Theoretical Computer Science - Approximation and online algorithms
A logical approach to multicut problems
Information Processing Letters
Improved Approximation Algorithms for Minimum Weight Vertex Separators
SIAM Journal on Computing
A fixed-parameter algorithm for the directed feedback vertex set problem
Journal of the ACM (JACM)
Expander flows, geometric embeddings and graph partitioning
Journal of the ACM (JACM)
Polynomial flow-cut gaps and hardness of directed cut problems
Journal of the ACM (JACM)
Constant ratio fixed-parameter approximation of the edge multicut problem
Information Processing Letters
Almost 2-SAT is fixed-parameter tractable
Journal of Computer and System Sciences
Clustering with partial information
Theoretical Computer Science
Breaking the Multicommodity Flow Barrier for O(vlog n)-Approximations to Sparsest Cut
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Algorithms for multiterminal cuts
CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications
Multicut algorithms via tree decompositions
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
FPT algorithms for path-transversal and cycle-transversal problems
Discrete Optimization
Finding odd cycle transversals
Operations Research Letters
Subset feedback vertex set is fixed-parameter tractable
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Clustering with local restrictions
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Multicut in trees viewed through the eyes of vertex cover
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Paths, flowers and vertex cover
ESA'11 Proceedings of the 19th European conference on Algorithms
A kernel of order 2k-clogk for vertex cover
Information Processing Letters
Compression via matroids: a randomized polynomial kernel for odd cycle transversal
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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
A golden ratio parameterized algorithm for cluster editing
IWOCA'11 Proceedings of the 22nd international conference on Combinatorial Algorithms
Important separators and parameterized algorithms
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
Restricted vertex multicut on permutation graphs
Discrete Applied Mathematics
On multiway cut parameterized above lower bounds
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
On polynomial kernels for structural parameterizations of odd cycle transversal
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Multicut in trees viewed through the eyes of vertex cover
Journal of Computer and System Sciences
What's next? future directions in parameterized complexity
The Multivariate Algorithmic Revolution and Beyond
Directed subset feedback vertex set is fixed-parameter tractable
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Clique cover and graph separation: new incompressibility results
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Fixed-parameter tractability of multicut in directed acyclic graphs
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Parameterized tractability of multiway cut with parity constraints
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
A golden ratio parameterized algorithm for Cluster Editing
Journal of Discrete Algorithms
Partitioning into colorful components by minimum edge deletions
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
Fixed-Parameter algorithms for finding agreement supertrees
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
Completely inapproximable monotone and antimonotone parameterized problems
Journal of Computer and System Sciences
Clustering with local restrictions
Information and Computation
On the parameterized complexity of finding separators with non-hereditary properties
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
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
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Given an undirected graph $G$, a collection {(s1,t1), ..., (sl,tl)} of pairs of vertices, and an integer p, the Edge Multicut problem ask if there is a set S of at most p edges such that the removal of S disconnects every si from the corresponding ti. Vertex Multicut is the analogous problem where S is a set of at most p vertices. Our main result is that both problems can be solved in time 2O(p3) ⋅ nO(1), i.e., fixed-parameter tractable parameterized by the size p of the cutset in the solution. By contrast, it is unlikely that an algorithm with running time of the form f(p) ⋅ nO(1) exists for the directed version of the problem, as we show it to be W[1]-hard parameterized by the size of the cutset.