The Complexity of Multiterminal Cuts
SIAM Journal on Computing
Polynomial time approximation schemes for dense instances of NP-hard problems
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
An O(log k) Approximate Min-Cut Max-Flow Theorem and Approximation Algorithm
SIAM Journal on Computing
Minimum 0-extensions of graph metrics
European Journal of Combinatorics
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
Divide-and-conquer approximation algorithms via spreading metrics
Journal of the ACM (JACM)
An improved approximation algorithm for MULTIWAY CUT
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
Information Processing Letters
Approximation algorithms for the 0-extension problem
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Approximate Max-Flow Min-(Multi)Cut Theorems and Their Applications
SIAM Journal on Computing
A 2-Approximation Algorithm for the Directed Multiway Cut Problem
SIAM Journal on Computing
An improved approximation algorithm for the 0-extension problem
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Optimal 3-Terminal Cuts and Linear Programming
Proceedings of the 7th International IPCO Conference on Integer Programming and Combinatorial Optimization
The regularity lemma and approximation schemes for dense problems
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Multiway cuts in node weighted graphs
Journal of Algorithms
Rounding Algorithms for a Geometric Embedding of Minimum Multiway Cut
Mathematics of Operations Research
A tight bound on approximating arbitrary metrics by tree metrics
Journal of Computer and System Sciences - Special issue: STOC 2003
A Linear Programming Formulation and Approximation Algorithms for the Metric Labeling Problem
SIAM Journal on Discrete Mathematics
The Hardness of Metric Labeling
SIAM Journal on Computing
Vertex cover might be hard to approximate to within 2-ε
Journal of Computer and System Sciences
Sdp gaps and ugc hardness for multiway cut, 0-extension, and metric labeling
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Expander flows, geometric embeddings and graph partitioning
Journal of the ACM (JACM)
On Earthmover Distance, Metric Labeling, and 0-Extension
SIAM Journal on Computing
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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The Multiway-Cut problem is a fundamental graph partitioning problem in which the objective is to find a minimum weight set of edges disconnecting a given set of special vertices called terminals. This problem is NP-hard and there is a well known geometric relaxation in which the graph is embedded into a high dimensional simplex. Rounding a solution to the geometric relaxation is equivalent to partitioning the simplex. We present a novel simplex partitioning algorithm which is based on em competing exponential clocks and distortion. Unlike previous methods, it utilizes cuts that are not parallel to the faces of the simplex. Applying this partitioning algorithm to the multiway cut problem, we obtain a simple (4/3)-approximation algorithm, thus, improving upon the current best known result. This bound is further pushed to obtain an approximation factor of 1.32388. It is known that under the assumption of the unique games conjecture, the best possible approximation for the Multiway-Cut problem can be attained via the geometric relaxation.