TY - JOUR

T1 - A tight approximation algorithm for the cluster vertex deletion problem

AU - Aprile, Manuel

AU - Drescher, Matthew

AU - Fiorini, Samuel

AU - Huynh, Tony

N1 - Funding Information:
This project was supported by ERC Consolidator Grant 615640-ForEFront. Samuel Fiorini and Manuel Aprile are also supported by FNRS grant T008720F-35293308-BD-OCP. Tony Huynh is also supported by the Australian Research Council.
Publisher Copyright:
© 2021, Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society.

PY - 2023/2

Y1 - 2023/2

N2 - We give the first 2-approximation algorithm for the cluster vertex deletion problem. This approximation factor is tight, since approximating the problem within any constant factor smaller than 2 is UGC-hard. Our algorithm combines previous approaches, based on the local ratio technique and the management of twins, with a novel construction of a “good” cost function on the vertices at distance at most 2 from any vertex of the input graph. As an additional contribution, we also study cluster vertex deletion from the polyhedral perspective, where we prove almost matching upper and lower bounds on how well linear programming relaxations can approximate the problem.

AB - We give the first 2-approximation algorithm for the cluster vertex deletion problem. This approximation factor is tight, since approximating the problem within any constant factor smaller than 2 is UGC-hard. Our algorithm combines previous approaches, based on the local ratio technique and the management of twins, with a novel construction of a “good” cost function on the vertices at distance at most 2 from any vertex of the input graph. As an additional contribution, we also study cluster vertex deletion from the polyhedral perspective, where we prove almost matching upper and lower bounds on how well linear programming relaxations can approximate the problem.

KW - Approximation algorithm

KW - Cluster vertex deletion

KW - Linear programming relaxation

KW - Sherali-Adams hierarchy

UR - http://www.scopus.com/inward/record.url?scp=85122367042&partnerID=8YFLogxK

U2 - 10.1007/s10107-021-01744-w

DO - 10.1007/s10107-021-01744-w

M3 - Article

AN - SCOPUS:85122367042

SN - 0025-5610

VL - 197

SP - 1069

EP - 1091

JO - Mathematical Programming

JF - Mathematical Programming

IS - 2

ER -