# Local Guarantees in Graph Cuts and Clustering

@inproceedings{Charikar2017LocalGI, title={Local Guarantees in Graph Cuts and Clustering}, author={Moses Charikar and Neha Gupta and Roy Schwartz}, booktitle={IPCO}, year={2017} }

Correlation Clustering is an elegant model that captures fundamental graph cut problems such as Min \(\,s-t\,\) Cut, Multiway Cut, and Multicut, extensively studied in combinatorial optimization. Here, we are given a graph with edges labeled \(+\) or − and the goal is to produce a clustering that agrees with the labels as much as possible: \(+\) edges within clusters and − edges across clusters. The classical approach towards Correlation Clustering (and other graph cut problems) is to optimize…

## 17 Citations

### Ju n 20 19 Min-Max Correlation Clustering via MultiCut ⋆

- Computer Science
- 2019

The first nontrivial approximation algorithm for correlation clustering is provided, achieving an O( √ logn ·max{log(|E|), log(k)}) approximation for general weighted graphs, where |E−| denotes the number of negative edges and k is thenumber of clusters in the optimum solution.

### Correlation clustering with local objectives

- Computer ScienceNeurIPS
- 2019

This paper presents the first known algorithm for minimizing the \ell_q norm of the disagreements vector on arbitrary graphs and provides an improved algorithm for minimize the\ell-q norm (q >= 1) of the disagreement vector on complete graphs.

### Improved algorithms for Correlation Clustering with local objectives

- Computer ScienceArXiv
- 2019

The first known algorithm for minimizing the $\ell_q$ norm of the disagreements vector on arbitrary graphs is presented and an improved algorithm for minimize the $q \geq 1$ norm on complete graphs is provided.

### Correlation Clustering with Sherali-Adams

- Computer ScienceArXiv
- 2022

This paper shows that there exists a (1 . 994+ ε )-approximation algorithm based on O (1 /ε 2 ) rounds of the Sherali-Adams hierarchy and reaches an approximation ratio of 2 + ε for Correlation Clustering.

### 𝓁p-norm Multiway Cut

- MathematicsESA
- 2021

It is shown that `p-norm-multiway-cut is NP-hard for constant number of terminals and isNP-hard in planar graphs and on the algorithmic side, an O(log n)approximation for all p ≥ 1 is designed.

### lp-Norm Multiway Cut

- Computer Science, Mathematics
- 2021

It is shown that lp-norm-multiway-cut is NP-hard for constant number of terminals and isNP-hard in planar graphs and an O(log2 n)-approximation for all p ≥ 1 is designed.

### Min-Max Correlation Clustering via MultiCut

- Computer ScienceIPCO
- 2019

The goal is to obtain a partitioning of the vertices that minimizes disagreements – weight of negative edges trapped inside a cluster plus positive edges between different clusters.

### Fixed Parameter Approximation Scheme for Min-max k-cut

- Computer ScienceIPCO
- 2021

The study of Minmax $k-cut is initiated by showing that it is NP-hard and W[1]-hard when parameterized by $k, and a parameterized approximation scheme when parameterization by $ k is designed.

### (cid:2) p -Norm Multiway Cut

- Mathematics, Computer Science
- 2022

(cid:2) p - norm - multiway - cut is shown to be NP-hard forconstantnumberofterminals and is NP- hard in planar graphs.

### Local Correlation Clustering with Asymmetric Classification Errors

- Computer ScienceICML
- 2021

An O ( (1/α)/2−/2p · log 1/α ) approximation algorithm is given for Correlation Clustering and an almost matching convex programming integrality gap is shown.

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