Correlation Clustering with Sherali-Adams - Archive ouverte HAL Accéder directement au contenu
Proceedings/Recueil Des Communications Année : 2022

Correlation Clustering with Sherali-Adams

Résumé

Given a complete graph $G = (V, E)$ where each edge is labeled $+$ or $-$, the Correlation Clustering problem asks to partition $V$ into clusters to minimize the number of $+$edges between different clusters plus the number of $-$edges within the same cluster. Correlation Clustering has been used to model a large number of clustering problems in practice, making it one of the most widely studied clustering formulations. The approximability of Correlation Clustering has been actively investigated [BBC04, CGW05, ACN08], culminating in a $2.06$-approximation algorithm [CMSY15], based on rounding the standard LP relaxation. Since the integrality gap for this formulation is 2, it has remained a major open question to determine if the approximation factor of 2 can be reached, or even breached. In this paper, we answer this question affirmatively by showing that there exists a $(1.994 + \epsilon)$-approximation algorithm based on $O(1/\epsilon^2$) rounds of the Sherali-Adams hierarchy. In order to round a solution to the Sherali-Adams relaxation, we adapt the {\em correlated rounding} originally developed for CSPs [BRS11, GS11, RT12]. With this tool, we reach an approximation ratio of $2+\epsilon$ for Correlation Clustering. To breach this ratio, we go beyond the traditional triangle-based analysis by employing a global charging scheme that amortizes the total cost of the rounding across different triangles.

Dates et versions

hal-03853109 , version 1 (15-11-2022)

Identifiants

Citer

Vincent Cohen-Addad, Euiwoong Lee, Alantha Newman. Correlation Clustering with Sherali-Adams. 2022, Proceedings of Symposium on Foundations of Computer Science (FOCS). ⟨hal-03853109⟩
25 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More