Approximation Algorithms for the Capacitated Min–Max Correlation Clustering Problem

2022 ◽  
Author(s):  
Sai Ji ◽  
Jun Li ◽  
Zijun Wu ◽  
Yicheng Xu
Keyword(s):  
Integer Programming ◽  
Approximation Algorithms ◽  
Approximation Algorithm ◽  
Gap Analysis ◽  
The Other ◽  
Correlation Clustering ◽  
Clustering Problem ◽  
Clustering Model ◽  
Proposed Model ◽  
Natural Variant

In this paper, we propose a so-called capacitated min–max correlation clustering model, a natural variant of the min–max correlation clustering problem. As our main contribution, we present an integer programming and its integrality gap analysis for the proposed model. Furthermore, we provide two approximation algorithms for the model, one of which is a bi-criteria approximation algorithm and the other is based on LP-rounding technique.

An FPT Algorithm for the Correlation Clustering Problem

2011 ◽  
Vol 474-476 ◽  
pp. 924-927 ◽  
Author(s):  
Xiao Xin
Keyword(s):  
Approximation Algorithms ◽  
Polynomial Time ◽  
Undirected Graph ◽  
Fixed Parameter Tractable ◽  
Correlation Clustering ◽  
Time Approximation ◽  
Running Time ◽  
Clustering Problem ◽  
Fpt Algorithm ◽  
Fixed Parameter

Given an undirected graph G=(V, E) with real nonnegative weights and + or – labels on its edges, the correlation clustering problem is to partition the vertices of G into clusters to minimize the total weight of cut + edges and uncut – edges. This problem is APX-hard and has been intensively studied mainly from the viewpoint of polynomial time approximation algorithms. By way of contrast, a fixed-parameter tractable algorithm is presented that takes treewidth as the parameter, with a running time that is linear in the number of vertices of G.

scholarly journals On Perturbation Resilience of Non-uniform k-Center

Algorithmica ◽  
2021 ◽  
Author(s):  
Sayan Bandyapadhyay
Keyword(s):  
Approximation Algorithm ◽  
Metric Space ◽  
The Other ◽  
Negative Numbers ◽  
Clustering Problem ◽  
Fixed Set ◽  
Tree Metrics ◽  
Perturbation Resilience ◽  
Minimum Dilation ◽  
Special Case

AbstractThe Non-Uniform k-center (NUkC) problem has recently been formulated by Chakrabarty et al. [ICALP, 2016; ACM Trans Algorithms 16(4):46:1–46:19, 2020] as a generalization of the classical k-center clustering problem. In NUkC, given a set of n points P in a metric space and non-negative numbers $$r_1, r_2, \ldots , r_k$$ r 1 , r 2 , … , r k , the goal is to find the minimum dilation $$\alpha $$ α and to choose k balls centered at the points of P with radius $$\alpha \cdot r_i$$ α · r i for $$1\le i\le k$$ 1 ≤ i ≤ k , such that all points of P are contained in the union of the chosen balls. They showed that the problem is $$\mathsf {NP}$$ NP -hard to approximate within any factor even in tree metrics. On the other hand, they designed a “bi-criteria” constant approximation algorithm that uses a constant times k balls. Surprisingly, no true approximation is known even in the special case when the $$r_i$$ r i ’s belong to a fixed set of size 3. In this paper, we study the NUkC problem under perturbation resilience, which was introduced by Bilu and Linial (Comb Probab Comput 21(5):643–660, 2012). We show that the problem under 2-perturbation resilience is polynomial time solvable when the $$r_i$$ r i ’s belong to a constant-sized set. However, we show that perturbation resilience does not help in the general case. In particular, our findings imply that even with perturbation resilience one cannot hope to find any “good” approximation for the problem.

scholarly journals Both Freud and Hoffman are Right: Anxious-Aggressive and Empathic Dimensions of Guilt

2008 ◽  
Vol 11 (1) ◽  
pp. 159-171 ◽  
Author(s):  
Itziar Etxebarria ◽  
Pedro Apodaca
Keyword(s):  
Young Adults ◽  
Subjective Experience ◽  
Negative Emotions ◽  
The Other ◽  
Point Scale ◽  
Nested Models ◽  
Proposed Model ◽  
Better Than

The purpose of the study was to confirm a model which proposed two basic dimensions in the subjective experience of guilt, one anxious-aggressive and the other empathic, as well as another dimension associated but not intrinsic to it, namely, the associated negative emotions dimension. Participants were 360 adolescents, young adults and adults of both sexes. They were asked to relate one of the situations that most frequently caused them to experience feelings of guilt and to specify its intensity and that of 9 other emotions that they may have experienced, to a greater or lesser extent, at the same time on a 7-point scale. The proposed model was shown to adequately fit the data and to be better than other alternative nested models. This result supports the views of both Freud and Hoffman regarding the nature of guilt, contradictory only at a first glance.

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