# A Randomized Approximation Scheme for Metric MAX-CUT

@article{Vega1998ARA, title={A Randomized Approximation Scheme for Metric MAX-CUT}, author={Wenceslas Fernandez de la Vega and Claire Mathieu}, journal={J. Comput. Syst. Sci.}, year={1998}, volume={63}, pages={531-541} }

Metric MAX-CUT is the problem of dividing a set of points in metric space into two parts so as to maximize the sum of the distances between points belonging to distinct parts. We show that metric MAX-CUT has a polynomial time randomized approximation scheme.

## 53 Citations

Complexity of the weighted max-cut in Euclidean space

- Mathematics
- 2014

The Max-Cut Problem is considered in an undirected graph whose vertices are points of a q-dimensional Euclidean space. The two cases are investigated, where the weights of the edges are equal to (i)…

A Parallel Approximation Algorithm for the Max Cut Problem on Cubic Graphs

- Computer Science, MathematicsASIAN
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The approximation ratio of the algorithm is 1:3 and improves the best known parallel approximation ratio, i.e. 2, in the special case of cubic graphs.

On greedy construction heuristics for the MAX-CUT problem

- Computer ScienceInt. J. Comput. Sci. Eng.
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A new 'worst-out' approach is studied and the proposed edge contraction heuristic is shown to have an approximation ratio of at least 1/3 and the results of experimental comparison of the worst-out approach, the well-known best-in algorithm, and modifications for both are included.

A Fully Polynomial-Time Approximation Scheme for a Special Case of a Balanced 2-Clustering Problem

- Computer Science, MathematicsDOOR
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An approximation algorithm is presented for the strongly NP-hard problem of partitioning a set of Euclidean points into two clusters and it is proved that it is a fully polynomial-time approximation scheme when the space dimension is bounded by a constant.

Polynomial-Time Approximation Algorithm for the Problem of Cardinality-Weighted Variance-Based 2-Clustering with a Given Center

- Computer Science, Mathematics
- 2018

A strongly NP-hard problem of partitioning a finite set of points of Euclidean space into two clusters is considered and a polynomial-time 2-approximation algorithm for solving the problem is constructed.

Approximability of the Minimum Bisection Problem: An Algorithmic Challenge

- Computer Science, MathematicsMFCS
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We survey some recent results on the complexity of computing approximate solutions for instances of the Minimum Bisection problem and formulate some very intriguing and still open questions about the…

Optimal Cuts and Bisections on the Real Line in Polynomial Time

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This paper solves the exact complexity of geometric cuts and bisections for dimension one (the real line) by designing an exact polynomial time algorithm based on a new technique of dealing with metric equalities and their connection to dynamic programming.

Approximation Schemes for Metric Clustering Problems

- Computer Science
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This work partitions a data set into a small number of clusters of related items and investigates their role in information retrieval and data analysis applications.

Clustering for edge-cost minimization (extended abstract)

- Computer Science, MathematicsSTOC '00
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A randomized approximation algorithm is obtained for partitioning a set of n points into clusters, so as to minimize the sum, over all intracluster pairs of points, of the cost associated with each pair.

Approximation Complexity of Nondense Instances of MAX-CUT

- Computer ScienceElectron. Colloquium Comput. Complex.
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We prove existence of approximation schemes for instances of MAXCUT with Ω( 2 ∆ ) edges which work in 2 O ( ∆ e2 ) nO(1) time. This entails in particular existence of quasi-polynomial approximation…

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